Yabu's formulae for hypergeometric $ _3F_2 $-series through Whipple's quadratic transformations

Abstract

By means of Whipple's quadratic transformations, two classes of hypergeometric $ _3F_2 $-series are expressed in terms of the Lerch transcendent function. Several difficult series with a free variable are explicitly evaluated in closed form, including Yabu's three remarkable identities.

Keywords

• hypergeometric series
• whipple's quadratic transformations
• the lerch transcendent function