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

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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