Some results on extended Hurwitz-Lerch zeta function

Komal Singh Yadav; Raj Karan Patel; Ashish Verma

Komal Singh Yadav Prof. Rajendra Singh (Rajju Bhaiya)Institute of Physical Sciences for Study and Research \\ V. B. S. Purvanchal University, Jaunpur (U.P.)- 222003, India
Raj Karan Patel Mahamaya Government Degree College Dhanupur, Handia\\ Prayagraj (U.P.)-221503, India
Ashish Verma Prof. Rajendra Singh (Rajju Bhaiya)Institute of Physical Sciences for Study and Research \\ V. B. S. Purvanchal University, Jaunpur (U.P.)- 222003, India

Abstract

This study investigates an extension of the extended Hurwitz-Lerch zeta function, along with related integral images and derivatives, by extending the extended beta function. Also established is a link between the extended Hurwitz-Lerch zeta function and the Laguerre polynomials. It is also demonstrated how to use the enlarged Hurwitz-Lerch zeta function $\zeta _{\nu,\lambda}^{\delta,\mu}(x;z,a;p,q)$ to probability distributions. Some (old and new) observations are offered here as specific illustrations of our theories.