New Transformation Formulae Of Quadratic $_7F_6$-Series

Abstract

The modified Abel lemma on summation by parts with the "remainder term"  is employed to investigate the partial sums of a quadratic $_7H_7$- series. Several unusual transformation formulae for these sums are established. As consequences, some new transformations of quadratic $_7F_6$-series are de duced, especially two of which respectively generalize two known $_3F_2(1)$-series summation formulae due to Watson and Whipple (1925).