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Definite Integral Involving Rational Functions of Powers and Exponentials Expressed in Terms of the Lerch Function [PDF]
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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Table in Gradshteyn and Ryzhik: Derivation of Definite Integrals of a Hyperbolic Function [PDF]
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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Definite Integrals using Orthogonality and Integral Transforms [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2012 We obtain definite integrals for products of associated Legendre functions with Bessel functions, associated Legendre functions, and Chebyshev polynomials of the first kind using orthogonality and integral transforms.
Howard S. Cohl, Hans Volkmer
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High precision computing of definite integrals with .net framework c# and x-mpir [PDF]
Cybernetics and Information Technologies, 2014 This paper concerns high precision numerical computing of definite integrals in a specific environment, namely .NET Framework. The work is a part of a series, tracing the progress of creating tools for high precision computations in this environment and ...
Dzhambov Velichko
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A Remarkable Definite Integral [PDF]
, 2013 An integral formula is developed which applies to an essentially arbitrary function. An application is made to the Riemann zeta function.
M. L. Glasser
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Fractional Definite Integral [PDF]
Fractal and Fractional, 2017 This paper proposes the definition of fractional definite integral and analyses the corresponding fundamental theorem of fractional calculus. In this context, we studied the relevant properties of the fractional derivatives that lead to such a definition.
Manuel Ortigueira, José Machado
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A family of definite integrals involving Legendre’s polynomials [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2023 The main objective of this article is to provide the analytical solutions (not previously found and not available in the literature) of some problems related with definite integrals integrands of which are the products of the derivatives of Legendre’s ...
M.I. Qureshi, S.H. Malik, D. Ahmad
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The definite neutrosophic integrals and its applications [PDF]
Neutrosophic Sets and Systems, 2022 the purpose of this article is to study the definite neutrosophic integrals, where the neutrosophic integrals are defined, in addition, set of theories and properties related to them were discussed, also, applications of the definite neutrosophic ...
Yaser Ahmad Alhasan
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Regular, Singular and Hypersingular Integrals over Fractal Contours
Mathematics, 2023 The paper is devoted to the approximate calculation of Riemann definite integrals, singular and hypersingular integrals over closed and open non-rectifiable curves and fractals.
Ilya Boykov +2 more
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Definite integral of the logarithm hyperbolic secant function in terms of the Hurwitz zeta function
AIMS Mathematics, 2021 We evaluate definite integrals of the form given by $\int_{0}^{\infty}R(a, x)\log (\cos (\alpha) \text{sech}(x)+1)dx$. The function $R(a, x)$ is a rational function with general complex number parameters.
Robert Reynolds, Allan Stauffer
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