The first goal of this paper is to give a new family of special function related to the Debye functions. By using these function and generating function method, we derive many novel formulas and relations involving the Debye functions, multiple Hurwitz Lerch zeta function which interpolate the Apostol-Bernoulli numbers...
We study a family of special numbers and polynomials introduced by Simsek whose exponential generating function has as denominator a falling factorial in the exponential variable. Using the partial fraction decomposition of this denominator, each member of the family is expressed by a single finite sum involving Bernou...
Hemen Dutta, G. Milovanović, Yılmaz Şimşek· 0 citations
The results obtained in this paper extend several identities and interpolation formulas previously established for the numbers y9,n(λ;a) to the higher-order case. We derive several explicit formulas, identities, and recurrence-type relations, and establish connections with well-known families of special numbers and pol...
Damla Gun, A. Bayad, Yılmaz Şimşek· Mathematics· 0 citations
This paper deals with a certain family of series which is derived from generating functions of the Frobenius-Euler and Apostol type polynomials and numbers. When special cases of this series are examined, it is shown that it generates some well-known families of zeta functions, such as the Hurwitz zeta and the Lerch ze...
Dora Pokaz, Mihaela Ribicic-Penava, Yılmaz Şimşek· RACSAM· 1 citation
We consider the N-tuple Hurwitz-Lerch zeta function introduced by Srivastava and Choi, ζN(s,x,λ)=∑k1,…,kN≥0λk1+⋯+kN(x+k1+⋯+kN)s, where N is a positive integer and λ is a complex parameter. A central breakthrough in this work is the explicit reduction of the N-tuple function to a linear combination of single Lerch trans...
Damla Gun, A. Bayad, Yılmaz Şimşek· Mathematics· 0 citations
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