Computation of the Mordell-Tornheim zeta values

Petojević, Aleksandar; Srivástava, H. M.

doi:10.1090/s0002-9939-08-09350-7

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Theorem 1 Let R Be a Positive Integer And Let1

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Cited by 4 publications

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“…There is preceding research [5,23,27,30,31] for the expression of the Mordell-Tornheim zeta function by integrals involving the polylogarithms or associated functions. For other expressions, refer to [11,21,22].…”

Section: Theorem 1 Let R Be a Positive Integer And Letmentioning

confidence: 99%

Generalized log sine integrals and the Mordell-Tornheim zeta values

Onodera

2010

Trans. Amer. Math. Soc.

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Section: Theorem 1 Let R Be a Positive Integer And Letmentioning

confidence: 99%

Generalized log sine integrals and the Mordell-Tornheim zeta values

Onodera

2010

Trans. Amer. Math. Soc.

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show abstract

Bibliography

2012

Zeta and Q-Zeta Functions and Associated Series and Integrals

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Integrals of logarithmic functions and alternating multiple zeta values

2019

Mathematica Slovaca

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By using the method of iterated integral representations of series, we establish some explicit relationships between multiple zeta values and Integrals of logarithmic functions. As applications of these relations, we show that multiple zeta values of the formfor p = 1 and 2, satisfy certain recurrence relations which allow us to write them in terms of zeta values, polylogarithms and ln 2. Moreover, we also prove that the multiple zeta values ζ(1, {1} m−1 , 3, {1} k−1 ) can be expressed as a rational linear combination of products of zeta values, multiple polylogarithms and ln 2 when m = k ∈ N. Furthermore, we also obtain reductions for certain multiple polylogarithmic values at 1 2 .

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Computation of the Mordell-Tornheim zeta values

Abstract: Abstract. In this paper the authors present several algorithmic formulas which are potentially useful in computing the following Mordell-Tornheim zeta values:for the special casesSome interesting (known or new) consequences and illustrative examples are also considered.

Cited by 4 publications

References 14 publications

Generalized log sine integrals and the Mordell-Tornheim zeta values

Generalized log sine integrals and the Mordell-Tornheim zeta values

Bibliography

Integrals of logarithmic functions and alternating multiple zeta values

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