A unified presentation of certain meromorphic functions related to the families of the partial zeta type functions and the L-functions

作者：Srivastava H M^*; Ozden Hacer; Cangul Ismail Naci; Simsek Yilmaz

来源：Applied Mathematics and Computation, 2012, 219(8): 3903-3913.

DOI：10.1016/j.amc.2012.10.025

• Bernoulli numbers and Bernoulli polynomials
• Euler numbers and Euler polynomials
• Genocchi numbers and Genocchi polynomials
• Riemann and Hurwitz (or generalized) zeta functions
• Hurwitz-Lerch, Lerch and Lipschitz-Lerch zeta functions
• Polylogarithm function
• Partial zeta type functions
• Dirichlet characters, Recurrence relations
• Mellin transformations

The aim of this paper is to construct a unified family of meromorphic functions, which is related to many known functions such as a unified family of partial zeta type functions, a unified family of L-functions, and so on. We investigate and derive many properties of this family of meromorphic functions. Moreover, we compute the residues of this family of meromorphic functions at their poles. We also give some applications and remarks involving this family of meromorphic functions.

• 出版日期2012-12-15