2022 年 65 巻 1 号 p. 35-61
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.
