On the generalized Hurwitz-Lerch zeta function and generalized Lambert transform
Copyright policy )On the generalized Hurwitz-Lerch zeta function and generalized Lambert transform
Summary: \textit{R. K. Raina} and \textit{H. M. Srivastava} [Rev. Téc. Fac. Ing., Univ. Zulia 18, No. 3, 301--304 (1995; Zbl 0851.11052)] introduced a generalized Lambert transform. \textit{S. P. Goyal} and \textit{R. K. Laddha} [Gaṇita Sandesh 11, No. 2, 99--108 (1997; Zbl 1186.11056)] have introduced generalizations of the Riemann zeta function and generalized Lambert transform. In the present paper, we introduce generalizations of the Hurwitz-Lerch zeta function and Lambert transform in a diverse direction. We derive generating functions involving generalized Hurwitz-Lerch zeta function. Connections between the generalized Lambert transform and generalized Hurwitz-Lerch zeta function are established. An inversion formula for the generalized Lambert transform is obtained. Some examples and special cases to illustrate our results are also mentioned.
Lambert transform, special functions, Mellin inversion theorem, generating functions, Riemann zeta function, Hurwitz and Lerch zeta functions, Bessel and Airy functions, cylinder functions, \({}_0F_1\), Hurwitz-Lerch zeta function
Lambert transform, special functions, Mellin inversion theorem, generating functions, Riemann zeta function, Hurwitz and Lerch zeta functions, Bessel and Airy functions, cylinder functions, \({}_0F_1\), Hurwitz-Lerch zeta function
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