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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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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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Journal of Mathematics, 2021 In this manuscript, the authors derive closed formula for definite integrals of combinations of powers and logarithmic functions of complicated arguments and express these integrals in terms of the Hurwitz zeta functions.
Robert Reynolds, Allan Stauffer
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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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The definite integrals of 2- refined neutrosophic functions and its properties [PDF]
Neutrosophic Sets and SystemsThis article aims to study the definite integrals of 2- refined neutrosophic functions and its properties. The definite integrals of 2- refined neutrosophic functions are defined in this study, and a set of theories are presented, including the ...
Yaser Ahmad Alhasan +2 more
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Fourier Series Formalization in ACL2(r) [PDF]
Electronic Proceedings in Theoretical Computer Science, 2015 We formalize some basic properties of Fourier series in the logic of ACL2(r), which is a variant of ACL2 that supports reasoning about the real and complex numbers by way of non-standard analysis.
Cuong K. Chau +2 more
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