A new generalization of the Riemann zeta function and its difference equation

Advances in Difference Equations

Asghar Qadir¹  Asifa Tassaddiq¹  Muhammad Aslam Chaudhry² 

[1] Center for Advanced Mathematics and Physics, National University of Science and Technology H-12, Islamabad, Pakistan;Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

关键词: Riemann zeta function;    Hurwitz zeta function;    Polylogarithm function;    Extended Fermi-Dirac;    Bose-Einstein;   

DOI  :  10.1186/1687-1847-2011-20

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We have introduced a new generalization of the Riemann zeta function. A special case of our generalization converges locally uniformly to the Riemann zeta function in the critical strip. It approximates the trivial and non-trivial zeros of the Riemann zeta function. Some properties of the generalized Riemann zeta function are investigated. The relation between the function and the general Hurwitz zeta function is exploited to deduce new identities.

【 授权许可】

CC BY