Transformations of basic hypergeometric series from the viewpoint of substitution of parameter operators

DOI10.1007/s11139-019-00145-0zbMath1428.33033OpenAlexW2951508152MaRDI QIDQ2337344

Jin Wang, Xin Rong Ma

Publication date: 19 November 2019

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-019-00145-0

zbMATH Keywords

orderlinear equationcompositionoperatorbasic hypergeometric seriesHeine's transformationWatson's transformationsubstitution of parameter operatorWeierstrass' theta function identity

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15)

Uses Software

• DLMF

Cites Work

• A connection formula for the \(q\)-confluent hypergeometric function
• On the equivalence of two fundamental theta identities
• Remarks on Some Basic Hypergeometric Series
• The Stokes phenomenon for the $q$-difference equation satisfied by the basic hypergeometric series ${}_3\varphi_1(a_1,a_2,a_3;b_1;q,x)$
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