Results 161 to 170 of about 133,643 (206)

New mock theta functions and formulas for basic hypergeometric series

Proceedings of the Edinburgh Mathematical Society, 2023
In recent years, mock theta functions in the modern sense have received great attention to seek examples of q-hypergeometric series and find their alternative representations.
O. X. Yao
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q-Supercongruences from squares of basic hypergeometric series

RACSAM, 2021
We give some new q-supercongruences on truncated forms of squares of basic hypergeometric series. Most of them are modulo the cube of a cyclotomic polynomial, and two of them are modulo the fourth power of a cyclotomic polynomial. The main ingredients of
Victor J. W. Guo, Long Li
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RESULTS ON BASIC HYPERGEOMETRIC SERIES AND CONTINUED FRACTIONS

JOURNAL OF RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES, 2022
In this paper, making use of certain known identities, we have established some result involving q-series and continued fractions.
G. S. Pant, K. B. Chand
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Application of basic hypergeometric series

Applied Mathematics and Computation, 2004
In this paper we use some concepts of basic hypergeometric series to give an extremely simple derivation of the exact formula for the expected number of nodes on level l in a random digital search tree, built from n random data.
Medhat A. Rakha, Essam S. El-Sedy
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Basic Hypergeometric Series: Author index

, 1990
Foreword Preface 1. Basic hypergeometric series 2. Summation, transformation, and expansion formulas 3. Additional summation, transformation, and expansion formulas 4. Basic contour integrals 5. Bilateral basic hypergeometric series 6. The Askey-Wilson q-
G. Gasper, Mizan Rahman
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Some q-supercongruences for truncated forms of squares of basic hypergeometric series

Journal of difference equations and applications (Print), 2020
Guo and Zudilin devised a method called ‘creative microscoping’ to establish many q-supercongruences for truncated basic hypergeometric series. Recently, El Bachraoui utilized the method of creative microscoping to derive some supercongruences for ...
Long Li
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Ramanujan and hypergeometric and basic hypergeometric series

Russian Mathematical Surveys, 1990
An incomplete survey of hypergeometric series is given, and some of Ramanujan's work on hypergeometric and basic hypergeometric series is put into the general framework as we understand it now.
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(q,h)-Bernstein Bases and Basic Hypergeometric Series

Journal of Engineering Technology and Applied Sciences
Quantum (q,h)-Bernstein bases and basic hypergeometric series are two seemingly unrelated mathematical entities. In this work, it is indicated that they are deeply interrelated theories.
Fatma Zürnacı Yetiş
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CAUCHY AUGMENTATION FOR BASIC HYPERGEOMETRIC SERIES

Bulletin of the London Mathematical Society, 2004
The authors present a technique of deriving basic hypergeometric identities from specializations using fewer parameters, by using the classical Cauchy identity on the expansion of the power of transformation formula. Moreover, a transformation formula analogous to Jackson's formula is obtained.
William Y. C. Chen, Amy M. Fu
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Almost poised basic hypergeometric series [PDF]

Proceedings of the Indian Academy of Sciences - Section A, 1987
Given a basic hypergeometric series with numerator parametersa1,a2, ...,ar and denominator parametersb2, ...,br, we say it isalmost poised ifbi, =a1qδ,iai,δi = 0, 1 or 2, for 2 ≤i ≤r. Identities are given for almost poised series withr = 3 andr = 5 when a1, =q−2n.
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