On hypergeometric-type generating relations associated with the generalized zeta function.
Bin-Saad, M.G., Al-Gonah, A.A. (2006)
Acta Mathematica Universitatis Comenianae. New Series
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Bin-Saad, M.G., Al-Gonah, A.A. (2006)
Acta Mathematica Universitatis Comenianae. New Series
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Raina, R.K., Chhajed, P.K. (2004)
Acta Mathematica Universitatis Comenianae. New Series
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Tibor K. Pogány, Arjun K. Rathie, Shoukat Ali (2012)
Matematički Vesnik
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Kuba, Markus (2007)
Séminaire Lotharingien de Combinatoire [electronic only]
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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 , 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 , 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,...
Tserendorj Batbold (2012)
Kragujevac Journal of Mathematics
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Tevzadze, T. (1996)
Georgian Mathematical Journal
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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...
Carsten Elsner, Shun Shimomura, Iekata Shiokawa (2009)
Journal de Théorie des Nombres de Bordeaux
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We present asymptotic representations for certain reciprocal sums of Fibonacci numbers and of Lucas numbers as a parameter tends to a critical value. As limiting cases of our results, we obtain Euler’s formulas for values of zeta functions.