A unified presentation of identities involving Weierstrass-type functions and their applications

In this work, we investigate and discuss Weierstrass-type functions ℘2k℘2k to the power of mm, and then derive a general formula for identities among them. Applications of this general formula include not only producing many of the familiar identities among Weierstrass-type functions, but also infinitely many new ones. Moreover, it is observed that new Bernoulli identities could be constructed systematically by means of the new identities among Weierstrass-type functions.