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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We provide evaluations of several recently studied higher and multiple Mahler measures using log-sine integrals. This is complemented with an analysis of generating functions and identities for log-sine integrals which allows the evaluations to be expressed in terms of zeta values or more general polylogarithmic terms. The machinery developed is then applied to evaluation of further families of...
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ژورنال
عنوان ژورنال: Journal of the Chungcheong Mathematical Society
سال: 2013
ISSN: 1226-3524
DOI: 10.14403/jcms.2013.26.4.769