منابع مشابه
Generalized Log Sine Integrals and the Mordell-tornheim Zeta Values
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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The Mahler measure of a polynomial in several variables has been a subject of much study over the past thirty years — very few closed forms are proven but more are conjectured. In the case of multiple Mahler measures more tractable but interesting families exist. Using values of log-sine integrals we provide systematic evaluations of various higher and multiple Mahler measures. The evaluations ...
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We continue our analysis of higher and multiple Mahler measures using log-sine integrals as started in [7, 8]. This motivates a detailed study of various multiple polylogarithms [4] and worked examples are given. Our techniques enable the reduction of several multiple Mahler measures, and supply an easy proof of two conjectures by Boyd.
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ژورنال
عنوان ژورنال: Honam Mathematical Journal
سال: 2013
ISSN: 1225-293X
DOI: 10.5831/hmj.2013.35.2.137