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

Year 2023, , 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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