## Richard Askey

University of Wisconsin-Madison, Professor Emeritus

480 Lincoln Drive

Madison, WI 53706

Telephone: (608 ) 263-7901, (608 ) 263-3053

EDUCATION:

Ph.D. Princeton University, 1961 M.A. Harvard University, 1956

B.A. Washington University, 1955

AREA OF SPECIALIZATION:

Special Functions

Srinivasa Ramanujan

EMPLOYMENT

Academic Positions:

University of Wisconsin-Madison, Professor Emeritus 2003-present

University of Wisconsin-Madison, John Bascom Professor of Mathematics 1995-2003

University of Wisconsin-Madison, Gabor Szegö Professor of Mathematics, 1986-1995

University of Wisconsin-Madison, Professor of Mathematics, 1968-1986

University of Wisconsin-Madison, Associate Professor of Mathematics, 1965-1968

University of Wisconsin-Madison, Assistant Professor of Mathematics, 1963-1965

University of Chicago, Instructor, 1961-1963

Washington University, Instructor, 1958-1961

Visiting Positions:

University of Paris VII, Physics Department, June 1993

University of Minnesota, March, 1988

University of Strasbourg, June, 1979

Mathematical Institute, Budapest, June 1973

Mathematical Center, Amsterdam, 1969-1970HONORS, AWARDS:

Guggenheim Fellow, 1969-1970

Honorary Fellow of Indian Academy of Sciences, Bangalore

Fellow of American Academy of Arts and Sciences

INVITED ADDRESSES TO MATHEMATICAL SOCIETIES:

Stieltjes Memorial Lecture, Dutch Mathematical Society, 1994

British Mathematical Colloquium, 1994

AAAS Lecture at MAA 75th Anniversary Meeting, 1990

Wisconsin Sectional Meeting of MAA, 1988

Illinois Sectional Meeting of MAA, 1987

Joint MAA and AMS meeting, 1985

Mathematical Association of America, 1984

International Congress of Mathematicians, 1983

Canadian Mathematical Society, 1981

Pi Mu Epsilon (J. Sutherland Frame Lecture), 1980

Ontario Mathematical Society, 1977

Society for Industrial and Applied Mathematics, 1969

American Mathematical Society, 1966

SERIES OF LECTURES:

Budapest, Turán Memorial Lectures, 1992

Pennsylvania State University:

Mathematics Department, College of Science Lectures, 1984

University of Illinois, Mathematics Department, Trjitzinsky Lectures, 1984

Regional Conference Lectures, 1974

INVITED LECTURES AT SPECIALIZED CONFERENCES

Year Place Topic of meeting

1965 Oberwolfach Integral transforms

1967 S.I.U., Edwardsville Orthogonal expansions

1969 Budapest Constructive theory of functions

1970 Oberwolfach Special Functions

1970 U. of Maryland Approximation theory

1971 Northwestern University I. J. Schoenberg’s Regional Conference

1972 Williams College Harmonic analysis on homogeneous spaces

1974 U. of New Haven Fractional calculus

1974 Oberwolfach Linear operators and approximations

1976 U. of Nebraska G. Weiss’s Regional Conference

1978 Oberwolfach Combinatorics

1979 Purdue Goffman meeting

1979 U. of East Carolina J. Dieudonne’s Regional Conference

1980 U. of Maryland Numerical Analysis and Special

Functions in Statistics

1982 U. of Waterloo Enumerative Combinatorics

1983 Oberwolfach Special Functions

1984 Turin Computations and special functions

1984 Bar Le Duc Orthogonal polynomials

1985 Purdue University Bieberbach proof celebration

1985 U. of Minnesota History and philosophy of mathematics

1985 U. of Quebec-Montreal Combinatorics

1986 Texas A. & M. Approximation Theory

1986 U. of Alberta Approximation Theory

1986 Stanford University Computers and Mathematics

1986 Weizmann Institute Gillis’s 75th birthday

1987 U. of Illinois Ramanujan

1987 Bowdoin College Theta Functions

1987 Nagano Real Variables

1987 Canberra Harmonic Analysis

1987 Annamali University Ramanujan Centenary

1987 Anna University Number Theory

1987 Madras Ramanujan Centenary Meeting

1987 Poona Univ. Ramanujan Analysis Meeting

1988 TIFR (Bombay) Number Theory

1988 IMA – Minneapolis q series

1988 Georgia Tech South East Approximation Theory

1988 Colorado Pade Approximation and Related Topics

1988 IMA-Minneapolis Signal Processing

1989 Valparaiso Computations and Function Theory

1989 St. John’s University Pi Mu Epsilon Meeting

1989 Winnipeg Asymptotics & Computational Analysis

1989 CWI Amsterdam Lie Algebras

1990 Tampa Approximation Theory

1990 Erice Orthogonal Polynomials

1991 Leningrad Approximation Theory

1991 Granada Orthogonal Polynomials

1991 Victoria Canadian Math. Soc. (Rooney meeting)

1992 New York Magnus Meeting

1992 U. of Kentucky Royster Meeting

1992 U. of Maine IWAA

1993 CWI Amsterdam Cohen – Koornwinder Day

1993 U. of Washington Hypergroups

1994 Montreal Integrability of Difference Equations

1994 U. Wisconsin-LaCrosse Mathematical Modelling

1994 U. Wisconsin Center- High School Problem Meeting

Richland Center

OTHER SCIENTIFIC ACTIVITIES

American Mathematical Society

Committee to choose hour speakers for central sectional meetings, 1974-1977, 1982-1983 Committee on committees, 1983-1984

Vice President 1986-1987

Committee on Mathematical History, 1987-1991 Committee on Libraries 1989-

Committee on Collected Works 1990-

Mathematical Association of America

Committee to choose Hedrick Lecturer, 1978-1980 Committee on The Chauvenet Prize, 1986-1988 Program Committee for San Antonio meeting Jan. 1993

AMS-MAA

Joint Committee for AMS-MAA Lecturers, January 1993, January 1994 SIAM

Editorial Board, SIAM Journal of Mathematical Analysis, 1969-1993 Polya Prize Committee, 1993

AMERICAN ASSOCIATION FOR ADVANCEMENT OF SCIENCE AMS representative to History and Philosophy of Science Section 1990-1992 Member at-large of

Mathematics Section Executive Committee, 1992-

Essays on Mathematics Education

Good Intentions are not Enough

RESEARCH GRANTS:

National Science Foundation, 1963-

Office of Naval Research, 1969-1970

PH.D. STUDENTS Carl Ganser, 1965

James Fitch, 1968

Cris Roosenraad, 1969

Susan Schindler, 1969

Robert Horton, 1973

Melinda Certain, 1974

Dennis Stanton, 1977

James Wilson, 1978

Daniel Moak, 1979

Walter Morris, 1982

Ismor Fischer, 1989

Warren Johnson, 1993

Shaun Cooper, 1995

BIBLIOGRAPHY

PUBLICATIONS

Weighted quadratic norms and ultraspherical polynomials. I, (with Isidore Hirschman, Jr.) Trans. Amer. Math. Soc. 91 (1959), 294-313. MR 21 #6494

Mean summability for ultraspherical polynomials (with I. Hirschman, Jr.), Math. Scand. 12 (1963), 167-177. MR 29 #1497

On some problems posed by Karlin and Szego concerning orthogonal polynomials, Bull. U. M. I. (3) 20 (1965), 125-127. MR 31 #1412

Mean convergence of expansions in Laguerre and Hermite series (with S. Wainger), Amer. J. Math. 87 (1965), 695-708. MR 32 #316

On the behavior of special classes of ultraspherical expansions, I. (with S. Wainger), J. d’Anal. Math 15 (1965), 193-220. MR 33 #1510

On the behavior of special classes of ultraspherical expansions, II. (with S. Wainger), J. d’Anal. Math 15 (1965), 221-244. MR 33 #1510

Orthogonal expansions with positive coefficients, Proc. Amer. Math Soc. 16 (1965), 1191-1194. MR 32 #2799

Integrability theorems for Fourier series (with S. Wainger), Duke Math. J. 33 (1966), 223-228. MR 33 #487

Orthogonal expansions of averaged functions, J. Math. Anal. Appl. 14 (1966), 326-331. MR 32 #6135

A transplantation theorem between ultraspherical series (with S. Wainger), Ill. J. Math. l0 (1966), 322-344. MR 35 #2069

A transplantation theorem for ultraspherical coefficients (with S. Wainger), Pac. J. Math. 16 (1966), 393-405. MR 36 #597

Norm inequalities for some orthogonal series, Bull. Amer. Math. Soc. 72 (1966), 808-823. MR 33 #6273

A transplantation theorem for Jacobi coefficients, Pac. J. Math. 21 (1967), 393-404. MR 36 #598

Smoothness conditions for Fourier series with monotone coefficients, Acta Sci. Math. 28 (1967), 169-171. MR 35 #3345

Fourier coefficients of positive functions (with R. P. Boas), Math Zeit. l00 (1967), 373-379. MR 36 #3042

Product of ultraspherical polynomials, Amer. Math Monthly 74 (1967), 1221-1222. MR 36 #6666

Jacobi polynomial expansions with positive coefficients and imbeddings of projective spaces, Bull. Amer. Math. Soc. 74 (1968), 301-304. MR #4039

Lp behavior of power series with positive coefficients, Proc. Amer. Math. Soc. 19 (1968), 303-305. MR 36 #6834

A dual convolution structure for Jacobi polynomials (with S. Wainger), Orthogonal Expansions and Their Continuous Analogues, edited by D. Haimo,

Southern Ill. Press, Edwardsville, 1968, 25-36. MR 38 #353

Positivity of the Cotes numbers for some ultraspherical abscissas (with J. Fitch), SIAM J. Numer. Anal. 5 (1968), 199-201. MR 37 #3750

On a positive trigonometric sum (with J. Fitch & G. Gasper), Proc. Amer. Math. Soc. 19 (1968), 1507. MR 37 #6662

Dual equations and classical orthogonal polynomials, J. Math. Anal. Appl. 24 (1968), 677-685. MR 38 #2553

A convolution structure for Jacobi series (with S. Wainger), Amer. J. Math. 91 (1969), 463-485. MR 41 #8728

Integral representations for Jacobi polynomials and some applications (with J. Fitch), J. Math. Anal. Appl. 26 (1969), 411-437. MR 38 #6128

A transplantation theorem for Jacobi series, Ill. J. Math. 13 (1969), 583-590. MR 39 #7344

Mehler’s integral for Pn (cos ), Amer. Math. Monthly 76 (1969), 1046-1049

An inequality for the classical polynomials, Indag. Math. 32 (1970), 22-25. MR 4l #2079

Some elementary integrability theorems for special transforms (with S.Karlin), J. d’Anal. Math. 23 (1970), 27-38. MR 42 #4971

Orthogonal polynomials and positivity, in Studies in Applied Math. 6, Special Functions and Wave Propagation, edited by D. Ludwig and F.W.J. Olver, SIAM,

Philadelphia, Pa., 1970, 64-85. MR 40 #624

Some integrability theorems for power series with positive coefficients (with R. P. Boas), in Math Essays dedicated to A. J. Macintyre edited by H. Shankar,

Ohio Univ. Press, 1970, 23-32. MR 43 #3689

Linearization of the product of orthogonal polynomials, in Problems in Analysis, edited by R. C. Gunning, Princeton Univ. Press, 1970, 131-138. MR 49 #9525

Linearization of the product of Jacobi polynomials. III, (with G. Gasper), Can. J. Math. 23 (197l), 332-338. MR 42 #8154

Jacobi polynomial expansions of Jacobi polynomials with non-negative coefficients (with G. Gasper), Proc. Phil. Soc. 70 (1971), 243-255. MR 45 #5430

Orthogonal expansions with positive coefficients. II, SIAM J. Math. Anal. 2 (1971), 340-346. MR 45 #5650

Positivity of the Cotes numbers for some Jacobi abscissas, Numer. Math. 19 (1972), 46-48. MR 46 #1052

Certain rational functions whose power series have positive coefficients (with G. Gasper), Amer. Math. Monthly 79 (1972), 327-341. MR 46 #599

Positive Jacobi polynomial sums, Tôhoku Math. J. 24 (1972), 109-119. MR 49 #5424

Jacobi summability, J. Approx. Th. 5 (1972), 387-392. MR 49 #982

Mean convergence of orthogonal series and Lagrange interpolation, Acta Math. Acad. Sci. Hung. 23 (1972), 71-85. MR 48 #762

A positive Cesaro mean (with James Fitch), Publ. Electrotech. Fac. Univ. Belgrade, No. 406, (1972), 131-134. MR 48 #9239

Grunbaum’s inequality for Bessel functions, J. Math. Anal Appl. 4l (1973), 122-124. MR 47 #53l7

An integral for Jacobi polynomials (with B. Razban), Simon Stevin 46 (1972-73), l65-l69. MR 48 #6502

Summability of Jacobi series, Trans. Amer. Math. Soc. 179 (1973), 71-84. MR 47 #3900

Refinements of Abel summability for Jacobi series, Proceedings of Symposia in Pure Mathematics, Vol. 26, Harmonic Analysis on Homogeneous Spaces,

edited by C. C. Moore, Amer. Math. Soc., Providence, R.I., 1973, 335-338. MR 49 #5684

Some positive trigonometric sums (with John Steinig), Trans. Amer. Math. Soc. l87 (1974), 295-307. MR 39 #3245

Certain rational functions whose power series have positive coefficients. II, SIAM J. Math. Anal. 5 (1974), 53-57. MR 48 #11897

Some absolutely monotonic and completely monotonic functions (with H. Pollard), SIAM J. Math. Anal. 5 (1974), 58-63. MR 49 #5685

Jacobi polynomials. I, New proofs of Koornwinder’s Laplace type integral representation and Bateman’s bilinear sum, SIAM J. Math. Anal. 5 (1974), 119-124.

MR 52 #6062

Positive Cesàro means of numerical series, Proc. Amer. Math. Soc. 45 (1974), 63-68. MR 49 #7644

Positive Jacobi polynomial sums, III, in Linear Operators and Approximation, II (P. L. Butzer and B. Sz.-Nagy, ed.) ISNM 25 (1974), Birkhauser, Basel and

Stuttgart, 305-312. MR 55 #3364

Some absolutely monotonic functions, Studia Sci. Math. Hung. 9 (1974), 51-56. MR 51 #8725.

A positive sum from summability theory (with G. Gasper and M. Ismail), J. Approx. Th. 13 (1975), 413-420. MR 51 #6207.

An inequality for Tchebycheff polynomials and extensions (with G. Gasper and L. Harris), J. Approx. Th. 14 (1975), 1-11. MR 51 #8501.

Some characteristic functions of unimodal distributions, J. Math. Anal. Appl. 50 (1975), 465-469. MR 51 #6910.

Inequalities via fractional integration, in Fractional Calculus and Its Applications, B. Ross, Ed., Lecture Notes in Mathematics, No. 457 (1975), Springer-Verlag,

106-115. MR 58 #1289.

A monotonic trigonometric sum (with J. Steinig), Amer. J. Math 98 (1976), 357-365. MR 53 #11288.

Permutation problems and special function (with M. Ismail), Canad. J. Math 28 (1976), 853-874. MR 53 #10594.

Positive Jacobi polynomial sums, II (with George Gasper), Amer. J. Math. 98 (1976), 709-737. MR 55 #3363.

Gaussian processes on compact symmetric spaces (with N.H.Bingham), Z. Wahrscheinlichkeitstheorie verw. Gebiete 37 (1976), 127-143. MR 54 #10984.

Convolution structures for Laguerre polynomials (with George Gasper), J. d’Anal. Math. 31 (1977), 48-68. MR 58 #6393.

Enumeration of partitions: The role of Eulerian series and q-orthogonal polynomials (with G. E. Andrews), Higher Combinatorics, M. Aigner (ed.), D. Reidel,

Dordrecht, Holland (1977), 3-26. MR 80b #10021.

Series inversions of some convolution transforms (with D. T. Haimo), J. Math. Anal. Appl. 59 (1977), 119-129. MR 56 #988.

Jacobi’s generating function for Jacobi polynomials, Proc. Amer. Math. Soc. 7l (1978), 243-246. MR 58 #6394.

Weighted permutation problems and Laguerre polynomials (with M. Ismail and T. Koornwinder), Journ. Combinatorial Theory, Series A 25 (1978), 277-287.

MR 80b: 33004.

A simple proof of Ramanujan’s summation of the 1 1 (with G. Andrews), Aequat. Math. l8 (1978), 333-337. MR 80h: 33004.

The q-gamma and q-beta functions, Applicable Analysis 8 (1978), 125-141. MR 80h: 33003.

Some absolutely monotonic functions, Acta Math. Acad. Sci. Hung. 33 (1979), 3-5. MR 80d: 33006

A set of orthogonal polynomials that generalize the Racah coefficients or 6-j symbols, (with J. Wilson), SIAM J. Math. Anal. l0 (1979), l008-l0l6, MR 80k:

33012

Positivity of the Cotes numbers for some Jacobi abscissas-II, J. Inst. Maths. Applics. 24 (1979), 95-98. MR 80e: 65028

The very well poised 6 6 ,(with M. Ismail) Proc. Amer. Math. Soc. 77 (1979), 218-222. MR 80m: 33002.

Ramanujan’s extensions of the gamma and beta functions, American Mathematical Monthly 87 (1980), 346-359. MR 82g: 01030

Some extensions of the gamma and beta functions, Real Analysis Exchange 4 (1980), 128-131.

The Rogers q-ultraspherical polynomials (with M. Ismail), Approximation Theory III (ed. E. W. Cheney), Academic Press, New York, (1980), 175-182.

Some basic hypergeometric extensions of integrals of Selberg and Andrews, SIAM J. Math. Anal. ll (1980), 938-951. MR 82e: 33002

Another q-extension of the beta function (with G. Andrews), Proc. Amer. Math. Soc. 8l (198l), 97-l00. MR 81j: 33001

A q-extension of Cauchy’s form of the beta integral, Quart. J. Math., Oxford (2) 32 (198l) 255-266. MR 82m: 33001

Hausdorff’s moment problem and expansions in Legendre polynomials (with I. J. Schoenberg and A. Sharma), J. Math. Anal. Appl. 86 (1982) 237-245. MR

83m: 44013

A set of hypergeometric orthogonal polynomials (with J. Wilson), SIAM J. Math. Anal. 13 (1982), 651-655. MR 83h: 33010

Two integrals of Ramanujan, Proc. Amer. Math. Soc. 85 (1982), 192-194. MR 83g: 3300l

An integral of products of Legendre functions and a Clebsch-Gordan sum, Letters in Math. Phys. 6 (1982), 299-302. MR 84a: 33018

A q-beta integral associated with BC1, SIAM J. Math. Anal. 13 (1982), 1008-1010. MR 84h: 17006b

A generalization of ultraspherical polynomials (with M. Ismail), Studies in Pure Mathematics, ed. P. Erdös, Birkhäuser, 1983, 55-78. MR 87a:33015

An elementary evaluation of a beta type integral, Indian J. Pure and Appl. Math. 14 (1983), 892-895. MR 84k:33003

A recurrence relation generalizing those of Apery, (with J. Wilson), J. Austral. Math. Soc. (Series A) 36 (1984), 267-278. MR 85h: 11007

Associated Laguerre and Hermite polynomials (with J. Wimp), Proc. Royal Soc. Edinburgh, 96A (1984), 15-37. MR 85f: 33014

The very well poised 6 6 II, Proc. Amer. Math. Soc. 90 (1984), 575-579. MR 85h: 33001

Recurrence relations, continued fractions and orthogonal polynomials (with M. Ismail), Memoirs of Amer. Math. Sec. (1984) #300, 108 pp. MR 85g: 33008

Remarks on the preceding paper by Gavin Brown and Edwin Hewitt, Math. Ann. 268 (1984), 123-126. MR 86e: 42016b

Sieved ultraspherical polynomials (with W. Al-Salam and W. R. Allaway), Trans. Amer. Math. Soc. 284 (1984), 39-55. MR 85j:33005

A characterization of the continuous q-ultraspherical polynomials (with W. Al-Salam and W. R. Allaway), Canadian Math. Bull. 27 (1984), 329-336. MR

86a:33007

Orthogonal polynomials old and new, and some combinatorial connections, in Enumeration and Design, ed, D. M. Jackson and S. A. Vanstone, Academic

Press, Orlando, 1984, 67-84. MR 87a:05022

Maximal degrees for Young diagrams in a strip (with A. Regev), Europ. J. Combinatorics 5 (1984), 189-191. MR 86c:05023

Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials (with J. Wilson), Memoirs of Amer. Math. Soc. (1985) #319, 55 pp.

MR 87a:05023

Orthogonal polynomials and some definite integrals, Proc. Internat. Congress of Mathematicians, Aug. 16-24, 1983, Warsawa, Warsaw 1985, 935-943. MR

86j:33012

Appendix (to chapter 12 of Ramanujan’s second notebook; continued fractions, by B. Berndt et al), Rocky Mountain J. Math. 15 (1985), 311-318. MR

87k:33004

Continuous Hahn polynomials, J. Phys. A: Math. Gen. 18 (1985), L1017-L1019. MR 87d:33021

Some problems about special functions and computations, Rendiconti del Seminario Matematico di Torino, special volume, 1985, 1-22.MR 87m:33001

Classical orthogonal polynomials (with George Andrews), Polynomes Orthogonaux et Applications, Proceedings, Bar-le-Duc 1984, ed. C. Brezinski et al,

Lecture Notes in Math., 1171 (1985), Springer, 36-62. MR 88c:33015b

An integral of products of ultraspherical functions and a q-extension (with T. H. Koornwinder and M. Rahman), J. London Math Soc. 33 (1986), 133-148. MR

87d:33020

Limits of some q-Laquerre polynomials, J. Approx. Th. 46 (1986), 213-216.MR 87i:33020

More q-beta integrals (with Ranjan Roy), Rocky Mountain J. Math 16 (1986), 365-372. MR 87f:33002

Inequalities for polynomials (with G. Gasper), The Bieberbach Conjecture, Proceedings of the Symposium on the Occasion of the Proof, ed. A. Baernstein II

et al, Mathematical Surveys and Monographs, 21, Amer.Math.Soc., Providence, 1986, 7-32.MR 88a:33003

Positive quadrature methods and positive polynomial sums, Approximation Theory V, ed Chui, Schumaker and Ward, Academic Press, Boston et al, 1986,

1-29. MR 88j:41065

Ramanujan’s 1 1 and formal Laurent series, Indian J. Math. 18 pages 29 (1987), 101-105. MR. 89c:33002.

An integral of Ramanujan and orthogonal polynomials, J. Indian Math. Soc. 51(1987), 27-36. MR 90d:33004

Ramanujan and important formulas, Srinivasa Ramanujan 1887-1920 a tribute, ed. K.R. Nagarajan and T. Soundararagan, Macmillan India Ltd., Madras,

1988, 32-41.

Beta integrals in Ramanujan’s papers, his unpublished work and further examples, in Ramanujan Revisited, ed. G. Andrews et at, Academic Press, Boston,

1988, 561-590. MR 89i:01044

How can mathematicians and mathematical historians help each other?, Proc. Conf. on History and Philosophy of Modern Mathematics, ed. W. Aspray and P.

Kitcher, Univ. of Minnesota Press, Minneapolis, 1988, 201-217. MR. 89i:01146

Beta integrals and q-extension, Proc. Ramanujan Centenial International Conference, ed. R. Balakrishnan, K. S. Padmanabhan and V. Thangaraj, Ramanujan

Mathematical Society, Annamalai Univ., Annamalainagar, 1988, 85-102. MR 90e:33004

Computer algebra and definite integrals, Computers Algebra, ed. D. Chudnovsky and R. Jenks, Dekker, New York, 1989, 121-129. MR 90h:33003

Orthogonal polynomials and theta functions, Theta Functions-Bowdoin 1987, ed. R. Gunning and L. Ehrenpreis, Amer. Math. Soc., Providence, 1989, vol. 2,

299-321. MR 90h:33006

Handbooks of special functions, A Century of Mathematics in America, part III, ed. P. Duren, Amer. Math. Soc., Providence, 1989, 369-391. MR 91h:33001

Continuous q-Hermite polynomials for q>1, q-Series and Partitions, ed. D. Stanton, Springer, New York, (1989) 151-158. MR 90h:33019

Beta integrals and the associated orthogonal polynomials, Number Theory, ed K. Alladi, Lecture Notes in Math, 1395 Springer, New York (1989) 84-121. MR

90k:33001

Divided difference operators and classical orthogonal polynomials, Rocky Mountain Math. J. 19 (1989), 33-37. MR 90h:33020

Selberg’s second beta integral and an integral of Mehta, (with D. Richards), Probability, Statistics and Mathematics: Papers in honor of Samuel Karlin,

Academic Press, Boston (1989) 27-39. MR 91f:33006

Ramanujan and hypergeometric and basic hypergeometric series, Ramanujan International Symposium on Analysis, ed. N. K.Thakare, (1989) Macmillan

India, Delhi, 1-83. Russian translation in Usp. Math. Nauk. 45(1) (1990), 33-76.

Variants of Clausen’s formula for the square of a special 2F1, Number Theory and Related Topics, Ramanujan colloquium, Bombay, (1988) Oxford Univ.

Press, Oxford, (1989) 1-12.

Graphs as an aid to understanding special functions, Asymptotics and Compututional Analysis, ed R. Wong, M. Dekker, New York, (1990), 3-33.

Relative extrema of Legendre functions of the second kind, Proc. Indian Acad. Sci. (Math. Sci.) (1990) 1-8. MR 91c:33008

Integration and Computers, Computers in Mathematics, ed. D.V. Chudnovsky and R.D. Jenks, M. Dekker, New York (1990), 35-82. MR 91k:33014

The number of representations of an integer as the sum of two squares, Indian J. Math., 32 (1990), 187-192. MR 91h:33026

The world of q , C.W.I. Quarterly, 5 (1993) 251-269.

The q-harmonic oscillator and an analogue of the Charlier polynomials, (with S.K. Suslov), J. Physics A., 26(1993), L693-698.

The q-harmonic oscillator and the Al-Salam and Carlitz polynomials, (with S.K. Suslov), Letters in Math. Phys., 29(1993), 123-132.

An analogue of the Fourier transform for a -harmonic oscillator (with N.M. Atakishiyev and S.K. Suslov), Symmetries in Science: Spectrum Generating

Algebras and Dynamics in Physics, ed. B. Gruber, Plenum, New York. (1993) 57-63.

Problems which interest and/or annoy me, in Journal of Computational and Applied Mathematics, 48(1993), 3-15.

An instance of Gaussian quadrature in Ramanujan’s Second Notebook, Proc. Indian Acad. Sci. (Math. Sect.) 104(1994), 237-243.

A look at the Bateman Project, The Mathematical Legacy of Wilhelm Magnus, ed. K. Kuken et al, Amer. Math. Soc. (1994) 29-43.

Fourier transformations for difference analogs of the harmonic oscillator (with N.M. Atakishiyev and S.K. Suslov), to appear in Proceedings of XV Workshop

on High Energy Physics and Field Theory, Protvino, Russia, 6-10 July, 1992.

Difference operators and orthogonal polynomials, Rendiconti di Matematica, Ser. VII 14 (1994), 135-144.

Fourier series and power series (with Deborah Haimo), American Mathematical Monthly, 103 (1996), 297-304.

On a general q-Fourier transform with nonsymmetric kernels, (with M. Rahman and S. Suslov), Journal of Computational and Applied Mathematics, 68

(1996), 25-55.

A brief introduction to the world of q, Symmetries and integrability of difference equations (Esterel, PQ, 1994), CRM Proc. Lecture Notes 9, Amer. Math. Soc.,

Providence, RI, (1996), 13-20.

A new look at some old trigonometric expansions, Harmonic analysis and nonlinear differential equations , Contemporary Math. 208, Amer. Math. Soc.,

Providence, RI, (1997), 73-84.

Vietoris’s inequalities and hypergeometric series, Recent Progress in Inequalities, Kluwer, (1998), 63-76. MR 99m:26023.

A class of non-orthogonal polynomials discovered by F.G. Tricomi, Tricomi’s Ideas and Contemporary Applied Mathematics, Atti dei Convegni Lincei 147,

Academia Nazionale dei Lincei (1998), 123-136.

Continued fractions and orthogonal polynomials, Analytic Number Theory to Constructive Approximations: A Volume in Honor of L.J. Lange, ed. B. Berndt

and F. Gesztesy, Cont. Math. 236, Amer. Math. Soc., Providence, 1999, 1-13.

Duality for classical orthogonal polynomials, J. Comput. Appl. Math., 178 (2005), no. 1-2, 37-43.

Evaluation of Sylvester type determinants using orthogonal polynomials, Advances in Analysis, Proceedings of the 4th International ISAAC Congress, ed.

H.G.W. Begehr et al, World Scientific, Singapore, (2005), 1-16.

BOOKS:

Orthogonal Polynomials and Special Functions, Regional Conference Series in Applied Mathematics, Vol. 21, Soc. Indust. and Appl. Math., Philadelphia, 1975.

MR 58 #1288

Theory and Application of Special Functions, editor, Academic Press, New York, 1975. MR 52 #819

G. Szegö, Collected Papers, Volumes 1, 2, 3. Editor, Birkhäuser Boston, 1982. MR 84d: 01082a-c

Special Functions: Group Theoretical Aspects and Applications, Editors, R. Askey, T. H. Koornwinder and W. Schempp, Reidel, Dordrecht, Holland, 1984.

Ramanujan Revisited, Editors G. Andrews, R. Askey, B. Berndt, K.G. Ramanathan and R. Rankin, Academic Press, Boston, 1988.

EXPOSITORY WRITING:

In fourth edition of McGraw Hill Encyclopedia of Science and Technology.

Hypergeometric functions

Legendre functions

Special functions.

Foreword to Willard Miller, Jr., Symmetry and Separation of Variables, Addison-Wesley, Reading, MA 1977

Retrospective on the Bateman Project, Applicable Analysis 8 (1978), 5-10.

Book review of George E. Andrews, The Theory of Partitions, Addison-Wesley, Reading, MA 1976, Bull. Amer. Math. Soc. (New Series) 1 (1979) 203-210.

Preface to Special Functions: Group Theoretical Aspects and Applications, Reidel, Dordrecht, Holland, 1984. MR 86c:33014

My reaction to de Branges’ proof of the Bieberbach Conjecture, The Bieberbach Conjecture, Proceedings of the Symposium on the Occasion of the Proof, ed,

A. Baernstein II et al, Mathematical Surveys and Mongraphs, 21, Amer. Math. Soc., Providence, 1986, 213-215.MR 88f:30001c

Book review of S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa, New Dehli 1988, Bull. Amer. Math. Soc. (New Series) 19 (1988),

558-560.

Book review of Pi and the AGM by Jonathan and Peter Borwein, Amer. Math. Monthly 95 (1988), 895-897.

Book review of Nathan J. Fine, Basic Hypergeometric Series and Applications, Bull. Amer. Math. Soc. (New Series) 20 (1989), 130-132.

Foreword to George Gasper and Mizan Rahman, Basic Hypergeometric Series, Cambridge Univ. Press, Cambridge, 1990.

In Memorium – I. J. Schoenberg (with C. de Boor), J. Approx. Th. 63 (1990), 1-2.

In Memorium – Antoni Zygmund, J. Approx. Theory, 71 (1992), 1-2.

Gabor Szego – 1895-1985 (with Paul Nevai) Mathematical Intelligencer, 18 No. 3 (1996), 10-22. Translated into Hungarian and republished in Matematikai

Lapok, 1993/3, 13-32.

Comments on Lars Onsager’s thesis, in “The Collected Works of Lars Onsager”, World Scientific, Singapore, 1996, 921-922.

Remembering Paul Turan, J. Approx. Theory, 86 (1996), 253-254.

Chandra and Ramanujan, Chandrasekhar, The Man Behind the Legend, ed. K.C. Wali, Imperial College Press, London, 1997, 130-138, (distributed by World

Scientific).

Romance in Mathematics: The case of S. Ramanujan, Wisconsin Academy Review, 45, no. 1, Winter, 1998-99, 13-16.

The work of George Andrews: A Madison perspective, in Seminaire Lotharingien de Combinatoire, B42b(1999), published on the web at

http://cartan.u-strasbg.fr/~slcl

EDUCATION WRITING:

Some comments on education, Notices of Amer. Math. Soc. 39 (1992), 424-426.

Book review of Japanese Grade 7-9 Mathematics, K. Kodaira, editor, The College Mathematics Journal, 23 (1992), 445-448.

The Japanese University Entrance Examinations in Mathematics, FOCUS, MAA Newsletter, 13, no. 1 (1993), 14.

Quantum: An Underused Resource, Wisconsin Teacher of Mathematics, Fall, 1994, 14-15.

Book review of Algebra, I. M. Gelfand and A. Shen, Amer. Math. Monthly 102 (1995), 78-81.

Cube root algorithms, Mathematics in School, (1995), 42-43.

What do we do about calculus? First do no harm, Amer. Math. Monthly 104 (1997), 738-743.

Mathematical content, an appendix to Steven G. Krantz’ “How to Teach Mathematics”, second edition, Amer. Math. Soc., Providence, 1998, 161-171.

The third mathematics education revolution, Contemporary Issues in Mathematics Education, ed. E. Gavosto, S. Krantz, W. McCallum, Cambridge Univ. Press,

1999, 95-107.

Why the Chinese Teach Math Better, Common Knowledge, vol. 12, nos. 1,2, Winter/Spring, 1999, 13.

Knowing and Teaching Elementary Mathematics, American Educator, vol. 23, no. 4, Fall, 1999, 6-13, 49.

Looking at Textbooks, Knowing and Learning Mathematics for Teaching, MSEB, National Academy Press, 2001, 106-125.