Some families of Weierstrass-type functions and their applications

Abstract

In this paper, we introduce the Weierstrass-type functions ℘2k and investigate some of their elementary properties in complex analysis. We focus upon the relations among the classical Weierstrass ℘-function and the Weierstrass-type functions ℘2k . By means of these relations, Rademacher's Bernoulli identity and several other identities can be deduced naturally and straightforwardly, except possibly the properties of the derivatives of the Weierstrass ℘-function. Our presentation provides a new direction to calculate a sub-class of Bernoulli identities without B 2.