Transformation formula for a double Clausenian hypergeometric series, its \(q\)-analogue, and its invariance group

DOI10.1016/S0377-0427(01)00389-2zbMath0994.33007MaRDI QIDQ5957969

Joris Van der Jeugt

Publication date: 14 October 2002

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

reductionsummation formulasinvariance grouptransformationbasic hypergeometric series

Mathematics Subject Classification ID

Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Other hypergeometric functions and integrals in several variables (33C70) Hypergeometric integrals and functions defined by them ((E), (G), (H) and (I) functions) (33C60) Other basic hypergeometric functions and integrals in several variables (33D70)

Related Items (8)

Some results for \(q\)-functions of many variables ⋮ Transformation and reduction formulae for double \(q\)-Clausen series of type \(\Phi_{1:1;\mu}^{1:2;\lambda}\) ⋮ Transformation and reduction formulae for doubleq-Clausen hypergeometric series ⋮ New transformation and reduction formulae for double \(q\)-Clausen series ⋮ Reduction and summation formulae for semi-terminating \(q\)-Kampé de Fériet series ⋮ Transformation and summation formulae for Kampé de Fériet series ⋮ A Method for q-Calculus ⋮ TRANSFORMATION AND REDUCTION FORMULAE FOR DOUBLE q-SERIES OF TYPE Φ^2:1;λ_2:0;μ

Cites Work

• Sums of certain double q-hypergeometric series
• Transformation and summation formulas for double hypergeometric series
• Some formulae for double Clausenian functions
• Hypergeometric series related to the \(9-j\) coefficient of \({\mathfrak{su}}(1,1)\)
• Transformation and summation formulas for Kampé de Fériet series \(F^{0:3}_{1:1} (1,1)\)
• Group theoretical basis of some identities for the generalized hypergeometric series
• Group theoretical basis for the terminating₃F₂(1) series
• Invariance groups of transformations of basic hypergeometric series
• Stretched 9-j coefficients and summation theorems
• Multiple hypergeometric functions and 9-j coefficients
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