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Integral expressions for Hilbert-type infinite multilinear form and related multiple Hurwitz-Lerch Zeta functions

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Author(s): Ram K. Saxena | Tibor Pogany

Journal: Journal of Interpolation and Approximation in Scientific Computing
ISSN 2194-3907

Volume: 2012;
Start page: 1;
Date: 2012;
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Keywords: Multiple Hurwitz-Lerch Zeta function | Hilbert-type infinite multilinear form | Multiple Hurwitz-Lerch Zeta power series | Tornheim's double sum | Mordell-Witten Zeta function | Matsumoto's multiple Mordell-Tornheim Zeta function | Dirichlet-series | Cahen's Laplace integral formula | Mellin-Barnes type integral

ABSTRACT
The article deals with different kinds integral expressions concerning multiple Hurwitz-Lerch Zeta function (introduced originally by Barnes ), Hilbert-type infinite multilinear form and its power series extension. Here Laplace integral forms and multiple Mellin-Barnes type integral representation are derived for these special functions. As a special cases of our investigations we deduce the integral expressions for the Matsumoto's multiple Mordell-Tornheim Zeta function, that is, for Tornheim's double sum i.e. Mordell-Witten Zeta, for the multiple Hurwitz Zeta and for the multiple Hurwitz-Euler Eta function, recently studied by Choi and Srivastava .
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