Unified presentation of p-adic L-functions associated with unification of the special numbers
Copyright policy )Unified presentation of p-adic L-functions associated with unification of the special numbers
\textit{H. Özden} [ICNAAM 2010, International Conference of Numerical Analysis and Applied Mathematics 2010, AIP Conf. Proc. 1281/2, 1125--1128 (2010), \url{doi:10.1063/1.3497848}] defined a generating function depending on parameters, in order to give a unified presentation of some well-known polynomials including the Apostol-Bernoulli polynomials, Apostol-Euler polynomials, and Apostol-Genocchi polynomials. For this generating function, the authors derive several partial differential equations (in different variables) and use them to obtain new functional equations and identities. Some linear combinations of the above unified constructions admit \(p\)-adic interpolation and are used to define \(p\)-adic \(L\)-functions generalizing those of various special kinds.
- Uludağ University Turkey
- Akdeniz University Turkey
General integral transforms, Genocchi number and polynomial, Riemann and Hurwitz (or generalized) zeta function, \(p\)-adic \(L\)-function, Zeta functions and \(L\)-functions, Dirichlet series, exponential series and other series in one complex variable, \(p\)-adic function, Euler number and polynomial, generating function, Bernoulli number and polynomial, partial zeta type function, Bernoulli and Euler numbers and polynomials, Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.), partial differential equation (PDE)
General integral transforms, Genocchi number and polynomial, Riemann and Hurwitz (or generalized) zeta function, \(p\)-adic \(L\)-function, Zeta functions and \(L\)-functions, Dirichlet series, exponential series and other series in one complex variable, \(p\)-adic function, Euler number and polynomial, generating function, Bernoulli number and polynomial, partial zeta type function, Bernoulli and Euler numbers and polynomials, Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.), partial differential equation (PDE)
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