Generalized log sine integrals and the Mordell-Tornheim zeta values

Onodera, Kazuhiro

doi:10.1090/S0002-9947-2010-05176-1

Generalized log sine integrals and the Mordell-Tornheim zeta values
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Trans. Amer. Math. Soc. 363 (2011), 1463-1485 Request permission

Abstract:

We introduce certain integrals of a product of the Bernoulli polynomials and logarithms of Milnor’s multiple sine functions. It is shown that all the integrals are expressed by the Mordell-Tornheim zeta values at positive integers and that the converse is also true. Moreover, we apply the theory of the integral to obtain various new results for the Mordell-Tornheim zeta values.

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