A basic bilateral series summation formula and its applications

DOI10.1080/10652469408819049zbMath0823.33009OpenAlexW2064938003MaRDI QIDQ4837528

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Publication date: 23 October 1995

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652469408819049

zbMATH Keywords

sums of squarestheta functionsbasic hypergeometric series

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15)

Related Items (8)

A reciprocity theorem for certain \(q\)-series found in Ramanujan's lost notebook ⋮ Partition implications of a three-parameter \(q\)-series identity ⋮ Unnamed Item ⋮ Some transformations on the bilateral series \(_2\psi_2\) ⋮ Unnamed Item ⋮ On a new summation formula for \(_{2}\psi _{2}\) basic bilateral hypergeometric series and its applications ⋮ Properties of the Appell-Lerch function (I) ⋮ Unnamed Item

Cites Work

• Unnamed Item
• The q-analogue of the Laguerre polynomials
• Ramanujan's ``lost notebook. I: Partial Theta-functions
• A simple proof of Ramanujan's summation of the \(_1\Psi_1\)
• Some eta-function identities deducible from Ramanujan's \(_ 1\Psi_ 1\) summation
• A Simple Proof of Fermat's Two-Square Theorem
• A Simple Proof of Jacobi's Two-Square Theorem
• Ramanujan's Extensions of the Gamma and Beta Functions
• A q-EXTENSION OF CAUCHY'S FORM OF THE BETA INTEGRAL
• Theq-Gamma andq-Beta Functions†
• An Introduction to Ramanujan's "lost" Notebook
• Beiträge zur Theorie der Heineschen Reihen. Die 24 Integrale der hypergeometrischen q‐Differenzengleichung. Das q‐Analogon der Laplace‐Transformation
• On Lerch's Transcendant and the Basic Bilateral Hypergeometric Series ₂ ψ₂
• ON THE BASIC BILATERAL HYPERGEOMETRIC SERIES ₂ψ₂

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