Keyword

basic hypergeometric series

Description: A basic hypergeometric series is a q-analogue of a hypergeometric series, defined by terms whose ratios involve powers of a parameter q.

Primary topic: Advanced Mathematical Identities (70%)

Wikidata ID: wiki/Q1062958

OpenAlex ID: keywords/basic-hypergeometric-series

Basic Hypergeometric Series

2004 · George Gasper, Mizan Rahman · Cambridge University Press eBooks · 3,609

Basic hypergeometric series

1991 · Walter Van Assche · Journal of Approximation Theory · 1,025

SPECIAL FUNCTIONS (Encyclopedia of Mathematics and its Applications 71)

2001 · Frits Beukers · Bulletin of the London Mathematical Society · 664

BASIC HYPERGEOMETRIC SERIES (Encyclopedia of Mathematics and its Applications)

1991 · T. H. Koornwinder · Bulletin of the London Mathematical Society · 616

Basic Hypergeometric Series and Applications

1988 · Nathan Fine · Mathematical surveys and monographs · 365

Overpartitions

2003 · Sylvie Corteel, Jeremy Lovejoy · Transactions of the American Mathematical Society · 363

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Basic Hypergeometric Series and Applications.

1990 · Ranjan Roy, Nathan J. Fine · American Mathematical Monthly · 327

Basic hypergeometric series

2004 · George Gasper, Mizan Rahman · Cambridge University Press eBooks · 319

A q-microscope for supercongruences

2019 · Victor J.W. Guo, Wadim Zudilin · Advances in Mathematics · 239

Proofs and Confirmations

1999 · David M. Bressoud · Cambridge University Press eBooks · 223

The Power of q

2017 · Michael D. Hirschhorn · Developments in mathematics · 148

Applications of 𝑞-Lagrange inversion to basic hypergeometric series

1983 · Ira Gessel, Dennis Stanton · Transactions of the American Mathematical Society · 127

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Some Eighth Order Mock Theta Functions

2000 · Basil Gordon, Richard J. Mcintosh · Journal of the London Mathematical Society · 112

More on the umbral calculus, with emphasis on the q-umbral calculus

1985 · Steven Roman · Journal of Mathematical Analysis and Applications · 109

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Mathematical Essays in honor of Gian-Carlo Rota

1998 · Sagan, Bruce, Stanley, Richard · Birkhäuser Boston eBooks · 108

Some q-Supercongruences from Transformation Formulas for Basic Hypergeometric Series

2020 · Victor J. W. Guo, Michael J. Schlosser · Constructive Approximation · 106

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Enumeration of Partitions: The Role of Eulerian Series and q-Orthogonal Polynomials

1977 · George E. Andrews, Richard Askey · Springer eBooks · 104

Parameter Augmentation for Basic Hypergeometric Series, II

1997 · William Y.C Chen, Zhi-Guo Liu · Journal of Combinatorial Theory Series A · 94

Asymptotic and generating relations for the q-Jacobi and 4φ3 polynomials

1982 · Mourad E.H Ismail, James A Wilson · Journal of Approximation Theory · 87

Special Functions 2000: Current Perspective and Future Directions

2001 · Springer eBooks · 86

Summations for basic hypergeometric series involving a q-analogue of the digamma function

1996 · C. Krattenthaler, H.M. Srivastava · Computers & Mathematics with Applications · 78

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Applications of q-Lagrange Inversion to Basic Hypergeometric Series

1983 · Ira Gessel, Dennis Stanton · Transactions of the American Mathematical Society · 74

Orthogonal Polynomials and Chevalley Groups

1984 · Dennis Stanton · Springer eBooks · 73

{Quantum Algebras and q-Special Functions Related to Coherent States Maps of the Disc

1998 · Anatol Odzijewicz · Communications in Mathematical Physics · 72

On Basic Hypergeometric Series, Mock Theta Functions, and Partitions (ii)

1966 · G. E. ANDREWS · The Quarterly Journal of Mathematics · 68

Works count: 1,034

Citation count: 15,470