Results 21 to 30 of about 11,866,753 (228)
A Note on an Octuple Integral in terms of the Lerch Function
European Journal of Pure and Applied Mathematics, 2022 The known exact expression for an octuple integral relating to research in the fields of mathematics and physics is summarized. A new closed form expression for this integral is given in terms of the Lerch function.
Robert Reynolds, Allan Stauffer
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European Journal of Pure and Applied Mathematics, 2022 Closed expressions using the Lerch function for a definite integral are derived and evaluated. Some of these closed expressions are given in Gradshteyn and Ryzhik. Some special cases of the integral are derived and discussed.
Robert Reynolds, Allan Stauffer
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Definite Integral of Power and Algebraic Functions in terms of the Lerch Function
European Journal of Pure and Applied Mathematics, 2021 Bierens de haan (1867) evaluated a definite integral involving the cotangent function and this result was also listed in Gradshteyn and Ryzhik (2007).
Robert Reynolds, Allan Stauffer
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A Note on the Definite Integral of the Lerch Function
European Journal of Pure and Applied Mathematics, 2021 This is a compilation of definite integrals involving the Lerch, Polylogarithm, Hurwitz functions and fundamental constants. Connections to previous work is compared and discussed. This collection of definite integrals is new in current literature.
Robert Reynolds, Allan Stauffer
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DEFINITE INTEGRAL OF LOGARITHMIC FUNCTIONS AND POWERS IN TERMS OF THE LERCH FUNCTION
Ural Mathematical Journal, 2021 A family of generalized definite logarithmic integrals given by $$\int_{0}^{1}\frac{\left(x^{ i m} (\log (a)+i \log (x))^k+x^{-i m} (\log (a)-i \log (x))^k\right)}{(x+1)^2}dx$$built over the Lerch function has its analytic properties and special values ...
Robert Reynolds, Allan Stauffer
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A Series Representation for the Hurwitz–Lerch Zeta Function
Axioms, 2021 We derive a new formula for the Hurwitz–Lerch zeta function in terms of the infinite sum of the incomplete gamma function. Special cases are derived in terms of fundamental constants.
Robert Reynolds, Allan Stauffer
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Note on a Stieltjes Transform in terms of the Lerch Function
European Journal of Pure and Applied Mathematics, 2021 In this work the authors derive the Stieltjes transform of the logarithmic function in terms of the Lerch function. This transform is used to derive closed form solutions involving fundamental constants and special functions.
Robert Reynolds, Allan Stauffer
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Symmetry, 2021 In this manuscript, the authors derive a double integral whose kernel involves the logarithmic function a polynomial raised to a power and a quotient function expressed it in terms of the Lerch function. All the results in this work are new.
Robert Reynolds, Allan Stauffer
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Symmetry, 2021 In this work, the authors use their contour integral method to derive an application of the Fourier integral theorem given by ∫−∞∞∫−∞∞emx−my−ex−ey+y(log(a)+x−y)kdxdy in terms of the Lerch function.
Robert Reynolds, Allan Stauffer
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Mellin Transform of an Exponential Fourier Transform Expressed in Terms of the Lerch Function
Mathematics and Statistics, 2021 The aim of this paper is to provide a table of definite integrals which includes both known and new integrals. This work is important because we provide a formal derivation for integrals in [7] not currently present in literature along with new integrals.
Robert Reynolds, Allan Stauffer
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