Education: A Golden Age

The best education in the world brought to students everywhere.

Richard Askey

University of Wisconsin-Madison, Professor Emeritus

480 Lincoln Drive
Madison, WI 53706
Telephone: (608 ) 263-7901, (608 ) 263-3053

Ph.D. Princeton University, 1961 M.A. Harvard University, 1956
B.A. Washington University, 1955
Special Functions
Srinivasa Ramanujan
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
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
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
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
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
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
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
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:
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
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

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
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
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
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.
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.
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),
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.
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