Three term relations for basic hypergeometric series

2017/03/26 by Yuka Suzuki, Suzuki, Yuka
Mathematics · #33D15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:33D15

paper · pdf · doi:10.48550/arxiv.1703.08753

16pages

arxiv created 2017/03/26 · arxiv updated 2017/03/28

Abstract

Any three basic hypergeometric series ₂phi₁ whose respective parameters (a, b, c) differ by integer powers of the base q satisfy a linear relation with coefficients which are rational functions of a, b, c, q and the variable x. These relations are called three term relations for the basic hypergeometric series ₂phi₁. This paper gives explicit expressions for the coefficients of these three term relations.

Related

• Symmetries of coefficients of three-term relations for basic hypergeometric series
• Symmetries of Coefficients of Three-Term Relations for the Hypergeometric Series
• Transformation formulas and three-term relations for basic hypergeometric series
• Basic hypergeometric identities derived from three-term relations
• Special values of the hypergeometric series