Some expansion formulas for a class of generalized Hurwitz–Lerch Zeta functions

By making use of fractional calculus, the authors present a systematic investigation of expansion and transformation formulas for several general families of the Hurwitz–Lerch Zeta functions. Relevant connections of the results discussed here with those obtained in earlier works are also indicated precisely.

[1]  A. Erdélyi,et al.  Tables of integral transforms , 1955 .

[2]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies) , 2006 .

[3]  W. Ames.  Mathematics in Science and Engineering , 1999 .

[4]  Edmund Taylor Whittaker,et al.  A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; with an Account of the Principal Transcendental Functions , 1920, Nature.

[5]  Hari M. Srivastava,et al.  Some relationships between the generalized Apostol–Bernoulli polynomials and Hurwitz–Lerch Zeta functions , 2006 .

[6]  Hari M. Srivastava,et al.  An explicit formula for the generalized Bernoulli polynomials , 1988 .

[7]  Hari M. Srivastava,et al.  Some formulas for the Bernoulli and Euler polynomials at rational arguments , 2000, Mathematical Proceedings of the Cambridge Philosophical Society.

[8]  A. Erdélyi,et al.  Higher Transcendental Functions , 1954 .

[9]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[10]  N. E. Nörlund.  Vorlesungen über Differenzenrechnung , 1924 .

[11]  Hari M. Srivastava,et al.  Remarks on some relationships between the Bernoulli and Euler polynomials , 2004, Appl. Math. Lett..

[12]  Hari M. Srivastava,et al.  A certain class of generating functions involving bilateral series , 2003, The ANZIAM Journal.

[13]  Hari M. Srivastava,et al.  Series Associated with the Zeta and Related Functions , 2001 .

[14]  I. Podlubny.  Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications , 1999 .

[15]  C. W. Clenshaw,et al.  The special functions and their approximations , 1972 .

[16]  Shy-Der Lin,et al.  Some families of the Hurwitz-Lerch Zeta functions and associated fractional derivative and other integral representations , 2004, Appl. Math. Comput..