Displaying similar documents to “Hypergeometric series associated with the Hurwitz-Lerch zeta function.”

On Witten multiple zeta-functions associated with semisimple Lie algebras I

Kohji Matsumoto, Hirofumi Tsumura (2006)

Annales de l’institut Fourier

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We define Witten multiple zeta-functions associated with semisimple Lie algebras 𝔰𝔩 ( n ) , ( n = 2 , 3 , ... ) of several complex variables, and prove the analytic continuation of them. These can be regarded as several variable generalizations of Witten zeta-functions defined by Zagier. In the case 𝔰𝔩 ( 4 ) , we determine the singularities of this function. Furthermore we prove certain functional relations among this function, the Mordell-Tornheim double zeta-functions and the Riemann zeta-function. Using these relations,...

Analytic and combinatoric aspects of Hurwitz polyzêtas

Jean-Yves Enjalbert, Hoang Ngoc Minh (2007)

Journal de Théorie des Nombres de Bordeaux

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In this work, a symbolic encoding of generalized Di-richlet generating series is found thanks to combinatorial techniques of noncommutative rational power series. This enables to explicit periodic generalized Dirichlet generating series – particularly the coloured polyzêtas – as linear combinations of Hurwitz polyzêtas. Moreover, the noncommutative version of the convolution theorem gives easily rise to an integral representation of Hurwitz polyzêtas. This representation enables us to...