Richard A. Askey

Richard A. Askey's AcademicInfluence.com Rankings

Richard A. Askey

Mathematics

#5627

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#7907

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Measure Theory

#850

World Rank

#1118

Historical Rank

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Mathematics

Richard A. Askey's Degrees

Bachelors Mathematics University of Chicago

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Richard A. Askey's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials (1985) (1159)
Orthogonal Polynomials and Special Functions (1975) (799)
Pi and the AGM (1999) (564)
Classical orthogonal polynomials (1985) (539)
ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS (1999) (466)
Special Functions: Partitions (1999) (348)
Recurrence relations, continued fractions, and orthogonal polynomials (1984) (263)
A Set of Orthogonal Polynomials That Generalize the Racah Coefficients or 6 - j Symbols. (1979) (261)
A generalization of ultraspherical polynomials (1983) (209)
Mean convergence of expansions in Laguerre and Hermite series (1965) (208)
HANDBOOK OF INTEGRAL TRANSFORMS OF HIGHER TRANSCENDENTAL FUNCTIONS: Theory and Algorithmic Tables (Ellis Horwood Series: Mathematics and Its Applications) (1983) (173)
Some Basic Hypergeometric Extensions of Integrals of Selberg and Andrews (1980) (152)
Special Functions by George E. Andrews (1999) (150)
Ramanujan's Extensions of the Gamma and Beta Functions (1980) (143)
Associated Laguerre and Hermite polynomials (1984) (129)
Enumeration of Partitions: The Role of Eulerian Series and q-Orthogonal Polynomials (1977) (119)
Theory and Application of Special Functions (1975) (111)
INTEGRAL REPRESENTATIONS FOR JACOBI POLYNOMIALS AND SOME APPLICATIONS. (1969) (105)
MULTIPLE GAUSSIAN HYPERGEOMETRIC SERIES (Ellis Horwood Series Mathematics and Its Applications) (1986) (103)
The q-Gamma and q-Beta Functions† (2007) (90)
On a general q -Fourier transformation with nonsymmetric kernels (1994) (86)
A CONVOLUTION STRUCTURE FOR JACOBI SERIES. (1969) (83)
Some positive trigonometric sums (1974) (81)
LECTURES ON HERMITE AND LAGUERRE EXPANSIONS (1994) (75)
Sieved ultraspherical polynomials (1984) (74)
Continuous q-Hermite Polynomials When q > 1 (1989) (74)
A Set of Hypergeometric Orthogonal Polynomials (1982) (74)
A century of mathematics in America (1988) (74)
Mean convergence of orthogonal series and Lagrange interpolation (1972) (73)
The q-harmonic oscillator and an analogue of the Charlier polynomials (1993) (72)
Convolution structures for Laguerre polynomials (1977) (71)
Another q-extension of the beta function (1981) (69)
POSITIVE JACOBI POLYNOMIAL SUMS (1972) (65)
Positive Jacobi Polynomial Sums, III (1976) (65)
Theq-harmonic oscillator and the Al-Salam and Carlitz polynomials (1993) (60)
A simple proof of Ramanujan’s summation of the1ψ1 (1978) (57)
On the behavior of special classes of ultraspherical expansions-I (1965) (56)
Integrability theorems for Fourier series (1966) (54)
Weighted Permutation Problems and Laguerre Polynomials (1978) (52)
Inequalities for polynomials (1986) (47)
Mean Summability for Ultraspherical Polynomials. (1963) (47)
Ramanujan and hypergeometric and basic hypergeometric series (1990) (46)
The Very Well Poised 6 ? 6 (1979) (45)
Special Functions: Group Theoretical Aspects and Applications (2001) (44)
Evaluation of Sylvester Type Determinants Using Orthogonal Polynomials (2005) (44)
Permutation Problems and Special Functions (1976) (43)
Jacobi polynomial expansions of Jacobi polynomials with non-negative coefficients (1971) (42)
More q-beta integrals (1986) (41)
Continuous Hahn polynomials (1985) (41)
Summability of Jacobi series (1973) (40)
Generalized hypergeometric functions and Meijer G-function (2010) (40)
An Integral of Ramanujan and Orthogonal Polynomials (1987) (39)
Orthogonal expansions with positive coefficients (1965) (39)
Orthogonal Expansions with Positive Coefficients. II (1971) (38)
Beta integrals and the associated orthogonal polynomials (1989) (37)
The very well poised (1979) (36)
Special Functions: The Gamma and Beta Functions (1978) (36)
Orthogonal polynomials and positivity (1969) (35)
Certain Rational Functions Whose Power Series Have Positive Coefficients (1972) (35)
Knowing and Teaching Elementary Mathematics. (1999) (32)
Some Absolutely Monotonic and Completely Monotonic Functions (1974) (31)
CHEBYSHEV POLYNOMIALS From Approximation Theory to Algebra and Number Theory (1991) (31)
An Integral of Products of Ultraspherical Functions and a q‐Extension (1986) (29)
An Analog of the Fourier Transformation for A q-Harmonic Oscillator (1993) (29)
A transplantation theorem for Jacobi series (1969) (28)
A transplantation theorem for ultraspherical coefficients. (1966) (27)
A transplantation theorem between ultraspherical series (1966) (26)
Learning from Assessment (2007) (25)
A q-EXTENSION OF CAUCHY'S FORM OF THE BETA INTEGRAL (1981) (24)
Hausdorff's moment problem and expansions in Legendre polynomials☆ (1982) (23)
Gabor Szegö: Collected Papers (1982) (22)
Two integrals of Ramanujan (1982) (22)
Jacobi Polynomials, I: New Proofs of Koornwinder's Laplace Type Integral Representation and Bateman's Bilinear Sum. (1974) (22)
Jacobi polynomial expansions with positive coefficients and imbeddings of projective spaces (1968) (22)
A transplantation theorem for Jacobi coefficients (1967) (20)
Limits of some q -Laguerre polynomials (1986) (20)
Positivity of the Cotes Numbers for Some Ultraspherical Abscissas (1968) (19)
Dual equations and classical orthogonal polynomials (1968) (19)
Grünbaum's inequality for Bessel functions (1973) (19)
Radial Characteristics Functions. (1973) (18)
Similarities Between Fourier and Power Series (1996) (17)
Positivity of the cotes numbers for some Jacobi abscissas (1972) (17)
Vietoris’s Inequalities and Hypergeometric Series (1998) (17)
Special Functions: The Selberg Integral and Its Applications (1999) (16)
A q-Beta Integral Associated with $BC_1 $ (1982) (15)
Certain Rational Functions Whose Power Series Have Positive Coefficients. II (1974) (15)
THE VERY WELL POISED 646 II (1984) (15)
Problems which interest and/or annoy me (1993) (14)
Divided difference operators and classical orthogonal polynomials (1989) (14)
Jacobi’s generating function for Jacobi polynomials (1978) (13)
Norm inequalities for some orthogonal series (1966) (13)
An integral of products of Legendre functions and a Clebsch-Gordan sum (1982) (12)
A positive sum from summability theory (1975) (11)
Selberg's Second Beta Integral and an Integral of Mehta (1989) (11)
Maximal Degrees for Young Diagrams in a Strip (1984) (11)
What Do We Do About Calculus? First, Do No Harm (1997) (11)
On the behaviour of special classes of ultraspherical expansions-II (1965) (11)
Review: Nathan J. Fine, Basic hypergeometric series and applications (1989) (10)
On a positive trigonometric sum (1968) (9)
A Note on the History of Series. (1975) (9)
Some characteristic functions of unimodal distributions (1975) (9)
Review: Srinivasa Ramanujan, The lost notebook and other unpublished papers (1988) (9)
SOME INTEGRABILITY THEOREMS FOR POWER SERIES WITH POSITIVE COEFFICIENTS. (1968) (9)
A recurrence relation generalizing those of Apéry (1984) (9)
Positivity of the Cotes Numbers for some Jacobi Abscissas—II (1979) (8)
Fibonacci and Related Sequences (2004) (8)
A brief introduction to the world of (1996) (8)
Weighted quadratic norms and ultraspherical polynomials. I (1959) (8)
The world of q (1992) (8)
The very well poised ₆₆. II (1984) (7)
A MONOTONIC TRIGONOMETRIC SUM. (1976) (7)
The Third Mathematics Education Revolution (1999) (7)
Theory and application of special functions : proceedings of an advanced seminar sponsored by the Mathematics Research Center, the University of Wisconsin-Madison, March 31-April 2, 1975 (1975) (7)
A Derangement Problem. (1975) (7)
Linearization of the Product of Jacobi Polynomials. III (1971) (7)
behavior of power series with positive coefficients (1968) (6)
Inequalities via fractional integration (1975) (6)
An inequality for the classical polynomials (1970) (6)
How can mathematicians and mathematical historians help each other (1988) (5)
The Work of George Andrews: A Madison Perspective (2001) (5)
Remarks on the preceding paper by Gavin Brown and Edwin Hewitt (1984) (5)
Graphs as an Aid to Understanding Special Functions (2020) (5)
Some elementary integrability theorems for special transforms (1970) (5)
Fourier coefficients of positive functions (1967) (4)
Lagrange Inversion Formula (1999) (4)
A Combinatorial Sum. (1975) (4)
Duality for classical orthogonal polynomials (2005) (4)
A Characterization of the Continuous q-Ultraspherical Polynomials (1984) (4)
An inequality for Tchebycheff polynomials and extensions (1975) (3)
On some problems posed by Karlin and Szegö concerning orthogonal polynomials. (1965) (3)
Eight lectures on orthogonal polynomials (1970) (3)
Completing Brahmagupta’s Extension of Ptolemy’s Theorem (2010) (3)
Review: Leonard Lewin, Polylogarithms and associated functions (1982) (3)
A simple proof of Ramanujans summation of the 1 ? 1 (1978) (3)
A Trigonometric Inequality (J. N. Lyness and C. B. Moler) (1969) (3)
Positive Cesàro means of numerical series (1974) (2)
Mehler's Integral for Pn(cos 0) (1969) (2)
Japanese Grade 7-9 Mathematics (1992) (2)
[54–6] Review of Higher Transcendental Functions, Vol. I and II (1982) (2)
The inequality of arithmetic and geometric means from multiple perspectives (2015) (2)
What Content Knowledge Should We Expect in Mathematics Education (2018) (2)
A Simple Proof of Ramanujan's Summation of the sub 1 psi sub 1. (1976) (2)
My reaction to de Branges’s proof of the Bieberbach conjecture (1986) (2)
Special Functions: Bessel Functions and Confluent Hypergeometric Functions (1999) (2)
Hypergeometric Functions and Their Applications (James B. Seaborn) (1992) (2)
Algebraic and analytic methods (2010) (2)
Delving Deeper: Fibonacci and Lucas Numbers. (2005) (2)
Multiple Hypergeometric Functions and Applications (Harold Exton) (1978) (2)
Relative extrema of Legendre functions of the second kind (1990) (2)
Commentary on a footnote (1988) (1)
Special Functions of Applied Mathematics (B. C. Carlson) (1979) (1)
Product of Ultraspherical Polynomials (1967) (1)
Advanced Problems: 6514-6517 (1986) (1)
Gaussian quadrature in Ramanujan’s Second Notebook (1994) (1)
10. Suggestions for Further Work (1975) (1)
Remembering Paul Turán (1996) (1)
Density Estimation and Bump-Hunting by the Penalized Likelihood Method Exemplified by Scattering and Meteorite Data: Comment (1980) (1)
BILINEAR ORTHOGONAL EXPANSIONS OF POSITIVE FUNCTIONS. (1968) (1)
Shorter Notes: On a Positive Trigonometric Sum (1968) (1)
Linearization of the Product οf Orthogonal Polynomials (2015) (1)
One-Sided Approximation to Special Functions (1974) (1)
Pi and the AGM. By Jonathan M. Borwein and Peter B. Borwein (1988) (1)
Series inversion of some convolution transforms (1977) (1)
ABSOLUTELY MONOTONIC FUNCTIONS (1979) (1)
On the Sign of a Set of Hypergeometric Functions (1986) (0)
Steele Prize for Mathematical Exposition (0)
Fourier Analysis and Approximation (Paul L. Butzer and Rolf J. Nessel) (1972) (0)
Phoenix Golf Club - Trophy Winners 2015 Juniors Competition Winner Runner Up Junior Captain's Drive In (2015) (0)
Special Functions: Bibliography (1999) (0)
3. Fractional Integrals and Hypergeometric Functions (1975) (0)
A Sine Inequality (1973) (0)
Special Functions: Topics in Orthogonal Polynomials (1999) (0)
A q-Extension of Cauchy’s Beta Integral (1984) (0)
7. Connection Coefficients (1975) (0)
8. Positive Sums (1975) (0)
Askey, Rokhlin Elected to NAS (1998) (0)
Gamma function (2010) (0)
Special Functions: Hypergeometric Transformations and Identities (1999) (0)
Some absolutely monotonic functions (1979) (0)
Advanced Problems: 6445-6447 (1983) (0)
Book Review: Basic hypergeometric series and applications (1989) (0)
Titles and Abstracts for the International Conference on Orthogonal Polynomials and q-Series May 10-12 , 2015 , University of Central Florida (2015) (0)
Summability and Fractional Integration (1999) (0)
An introduction to orthogonal polynomials: T. S. Chihara, Gordon & Breach, New York/ London/Paris, 1978, 249 pp (1985) (0)
Basic Hypergeometric Extensions of Some Integrals (1985) (0)
Special Functions: Spherical Harmonics (1999) (0)
Letters to the editor (1987) (0)
Review: The Mathematics that Every Secondary School Math Teacher Needs to Know. Routledge, New York and London, 2010, xxvii + 732 pp., ISBN 978-0-415-99413-2 (pbk), $89.95. by Alan Sultan and Alice F. Artzt (2011) (0)
6. Rational Functions with Positive Power Series Coefficients (1975) (0)
Fractional sum and fractional difference on non-uniform lattices and analogue of Euler and Cauchy Beta formulas (2021) (0)
Special Issue on Orthogonal Polynomials and Computer Algebra (1999) (0)
5. Linearization of Products (1975) (0)
MISCELLANEA (1920) (0)
1. Classical Results for Trigonometric Polynomials and Fourier Series and Other Isolated Results (1975) (0)
Special Functions: Orthogonal Polynomials (1999) (0)
A NEW CLASS OF ORTHOGONAL POLYNOMIALS1 (1984) (0)
Review: George E. Andrews, The theory of partitions (1979) (0)
Integration and Computers (2020) (0)
Dedicated to Professor Gen-ichirδ Sunouchi on his 60th birthday (2021) (0)
Orthogonal expansions of averaged functions (1966) (0)
Approximation with Rational Functions (D. J. Newman) (1981) (0)
Chandra and Ramanujan (1997) (0)
2 Blumenthal – Nevai theorems for the one quarter class of orthogonal polynomials Posed (2016) (0)
Special Functions: Introduction to q -Series (1999) (0)
Mizan Rahman, His Mathematics and Literary Writings (2005) (0)
On the Sign of a Set of Hypergeometric Functions (Richard Askey) (1987) (0)
Special Functions: Euler–Maclaurin Summation Formula (1999) (0)
Handbook of Hypergeometric Integrals: Theory, Applications, Tables, Computer Programs (Harold Exton) (1979) (0)
Special Functions: The Hypergeometric Functions (1999) (0)
Combinatory Analysis 2008 : Partitions , q-series , and Applications (1998) (0)
[50–5] On the Relative Extrema of Legendre Polynomials (1982) (0)
The H-Function with Applications in Statistics and other Disciplines (A. M. Mathai and R. K. Saxena) (1980) (0)
A Positive Integral (1969) (0)
4. Addition Formulas (1975) (0)
Number theory and related topics : papers presented at the Ramanujan Colloquium, Bombay 1988 (1989) (0)
Advanced Problems: 6451-6453 (1984) (0)
Three notes on orthogonal polynomials (1969) (0)
2. Jacobi Polynomial Series (1975) (0)
Reviews (2011) (0)
Some Elementary Uses of Complex Numbers (2011) (0)
Special Functions: Special Orthogonal Polynomials (1999) (0)
Advanced Problems: 6496-6497 (1985) (0)
Antoni Zygmund (December 26, 1900–May 30, 1992) (1992) (0)
Tables of Bessel Transforms (Fritz Oberhettinger); Fourier Expansions: A Collection of Formulas (Fritz Oberhettinger); Fourier Transforms of Distributions and Their Inverses—A Collection of Tables (Fritz Oberhettinger); Tables of Laplace Transforms (F. Oberhettinger and L. Badii) (1975) (0)
Series Solutions of Differential Equations (1999) (0)
9. More Positive Sums and Applications (1975) (0)
MEAN CONVERGENCE ON ORTHOGONAL SERIES AND CONJUGATE SERIES (1961) (0)
Ted Chihara and his work on orthogonal polynomials (2001) (0)
[55–1] On Algebraic Equations with Integral Coefficients Whose Roots Belong to a Given Point Set (1982) (0)
Handbook of series for scientists and engineers : Visvaldis Mangulis. 134 pages, diagrams, 6 × 9 in. New York, Academic Press Inc., 1965. Price, $6.95. (1969) (0)
A generalization of ultraspherical polynomials. Summary report (1978) (0)

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Cornell University

Richard A. Askey's Academic­Influence.com Rankings