Transformation formulae for terminating balanced $_4F_3$-series and implications

Year 2023, Volume: 52 Issue: 2, 391 - 397, 31.03.2023

Wenchang Chu

https://doi.org/10.15672/hujms.1116891

Abstract

A new transformation from terminating balanced $_4F_3$-series to $_3F_2$-series is proved that contains a few known summation formulae as special cases. By means of Whipple's transformation, further closed form evaluations are given for terminating well--poised $_7F_6$-series as applications.

Keywords

Classical hypergeometric series , balanced series , well–poised series , Whipple’s formula , Pfaff–Saalschütz formula

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