𝑞-extension of the 𝑝-adic gamma function. II

Abstract

Taylor series and asymptotic expansions are developed for q q -extensions of the p p -adic psi (derivative of log-gamma) function "twisted" by roots of unity. Connections with p p -adic L L -functions and q q -expansions of Eisenstein series are discussed. The p p -adic series are compared with the analogous classical expansions.