A \(q\)-analogue of Appell's \(F_ 1\) function, its integral representation and transformations

DOI10.2140/pjm.1990.142.121zbMath0638.33003OpenAlexW2048132817MaRDI QIDQ1099308

B. Nassrallah

Publication date: 1990

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.pjm/1102646465

zbMATH Keywords

basic hypergeometric series

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) (q)-gamma functions, (q)-beta functions and integrals (33D05)

Cites Work

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• A q-analogue of Appell's \(F_ 1\) function and some quadratic transformation formulas for non-terminating basic hypergeometric series
• Some expansions involving basic hypergeometric functions of two variables
• Some relations between basic hypergeometric functions of two variables
• A Simple Evaluation of Askey and Wilson's q-Beta Integral
• Projection Formulas, a Reproducing Kernel and a Generating Function for q-Wilson Polynomials
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• An integral Representation of a ₁₀ϕ₉ and Continuous Bi-Orthogonal ₁₀ϕ₉ Rational Functions
• Some Remarks on q-Beta Integral
• Theq-Gamma andq-Beta Functions†
• Summations and Transformations for Basic Appell Series
• Transformations of Basic Hypergeometric Functions of Special Type
• ON BASIC DOUBLE HYPERGEOMETRIC FUNCTIONS
• BASIC DOUBLE HYPERGEOMETRIC FUNCTIONS (II)

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