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Integral and Series Representations of Riemann's Zeta Function and Dirichlet's Eta Function and a Medley of Related Results [PDF]
Journal of Mathematics, 2013 Contour integral representations of Riemann's Zeta function and Dirichlet's Eta (alternating Zeta) function are presented and investigated. These representations flow naturally from methods developed in the 1800s, but somehow they do not appear in the ...
Michael S. Milgram
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Axioms, 2021 A class of definite integrals involving a quotient function with a reducible polynomial, logarithm and nested logarithm functions are derived with a possible connection to contact problems for a wedge.
Robert Reynolds, Allan Stauffer
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Infinite Sum of the Incomplete Gamma Function Expressed in Terms of the Hurwitz Zeta Function
Mathematics, 2021 We apply our simultaneous contour integral method to an infinite sum in Prudnikov et al. and use it to derive the infinite sum of the Incomplete gamma function in terms of the Hurwitz zeta function.
Robert Reynolds, Allan Stauffer
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Journal of Low Frequency Noise, Vibration and Active Control, 2021 This paper presents a numerical approach for the determination of scattering frequencies of two-dimensional acoustic exterior resonance problems using boundary element method combined with a contour integral method.
Haifeng Gao +4 more
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The Logarithmic Transform of a Polynomial Function Expressed in Terms of the Lerch Function
Mathematics, 2021 This is a collection of definite integrals involving the logarithmic and polynomial functions in terms of special functions and fundamental constants. All the results in this work are new.
Robert Reynolds, Allan Stauffer
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Table in Gradshteyn and Ryzhik: Derivation of Definite Integrals of a Hyperbolic Function
Sci, 2021 We present a method using contour integration to derive definite integrals and their associated infinite sums which can be expressed as a special function. We give a proof of the basic equation and some examples of the method.
Robert Reynolds, Allan Stauffer
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Mathematical and Computational Applications, 2021 This paper gives new integrals related to a class of special functions. This paper also showcases the derivation of definite integrals involving the quotient of functions with powers and the exponential function expressed in terms of the Lerch function ...
Robert Reynolds, Allan Stauffer
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Targeting multi-loop integrals with neural networks
SciPost Physics, 2022 Numerical evaluations of Feynman integrals often proceed via a deformation of the integration contour into the complex plane. While valid contours are easy to construct, the numerical precision for a multi-loop integral can depend critically on the ...
Ramon Winterhalder, Vitaly Magerya, Emilio Villa, Stephen P. Jones, Matthias Kerner, Anja Butter, Gudrun Heinrich, Tilman Plehn
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SciPost Physics, 2023 The work fluctuation theorem (FT) is a symmetry connecting the moment generating functions (MGFs) of the work extracted in a given process and in its time-reversed counterpart.
Vasco Cavina, Sadeq S. Kadijani, Massimiliano Esposito, Thomas L. Schmidt
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Backpropagating Hybrid Monte Carlo algorithm for fast Lefschetz thimble calculations
Journal of High Energy Physics, 2022 The Picard-Lefschetz theory has been attracting much attention as a tool to evaluate a multi-variable integral with a complex weight, which appears in various important problems in theoretical physics.
Genki Fujisawa +3 more
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