Transformation Formulas and Three-Term Relations for Basic Hypergeometric Series

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Abstract

<p>We derive two generalizations of Gasper's transformation formula for basic hypergeometric series. Using these generalized transformation formulas, we give explicit expressions for the coefficients of three-term relations for the basic hypergeometric series 2φ1, which are generalizations of the author's previous results on three-term relations for 2φ1. These generalized three-term relations involve multiplying the variable of one of the three 2φ1 by a power of q. Also, as corollaries of the generalizations of Gasper's transformation formula, we derive a few generalizations of Gasper's summation formulas for basic hypergeometric series.</p>

Journal

  • Funkcialaj Ekvacioj

    Funkcialaj Ekvacioj 65 (1), 35-61, 2022-04-15

    Division of Functional Equations, The Mathematical Society of Japan

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