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Cauchy Principal Value Contour Integral with Applications [PDF]
Entropy, 2017 Cauchy principal value is a standard method applied in mathematical applications by which an improper, and possibly divergent, integral is measured in a balanced way around singularities or at infinity.
Matilde Legua, Luis M. Sánchez-Ruiz
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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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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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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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Resultants and contour integrals [PDF]
Functional Analysis and Its Applications, 2012 9 ...
Morozov, A., Shakirov, Sh.
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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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Contour Integration for Eigenvector Nonlinearities
SIAM Journal on Matrix Analysis and Applications, 2023 24 pages, 6 ...
Claes, Rob +2 more
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The Analysis of Contour Integrals [PDF]
Abstract and Applied Analysis, 2008 For any n, the contour integral s2 = −λ, is associated with differential equation d2y(x)/dx2 + (λ + n(n + 1)/cosh2x)y(x) = 0. Explicit solutions for n = 1 are obtained. For n = 1, eigenvalues, eigenfunctions, spectral function, and eigenfunction expansions are explored.
Tanriverdi, Tanfer, Mcleod, JohnBryce
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