Some families of Weierstrass-type functions and their applications
- 1 September 2008
- journal article
- research article
- Published by Taylor & Francis in Integral Transforms and Special Functions
- Vol. 19 (9) , 621-632
- https://doi.org/10.1080/10652460802230546
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.Keywords
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