Results 11 to 20 of about 92,147 (297)
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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An extension of the method of brackets. Part 1 [PDF]
Open Mathematics, 2017 The method of brackets is an efficient method for the evaluation of alarge class of definite integrals on the half-line. It is based on a small collection of rules, some of which are heuristic.
Gonzalez Ivan +3 more
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Relation of the Cyclotomic Equation with the Harmonic and Derived Series [PDF]
The Scientific World Journal, 2015 We associate some (old) convergent series related to definite integrals with the cyclotomic equation xm-1=0, for several natural numbers m; for example, for m=3, x3-1=(x-1)(1+x+x2) leads to ∫01dx(1/(1+x+x2))=π/(33)=(1-1/2)+(1/4-1/5)+(1/7-1/8)+⋯.
Luis J. Boya, Cristian Rivera
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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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Derivation of some integrals in Gradshteyn and Ryzhik
AIMS Mathematics, 2021 In this work we present derivations of the formula listed in entry 4.113 in the sixth edition of Gradshteyn and Rhyzik's table of integrals. We evaluate two definite integrals of the formandin terms of the Lerch function where $ k $, $ a $, $ z $ and
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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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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A Lost Theorem: Definite Integrals in Asymptotic Setting [PDF]
, 2008 We present a simple yet rigorous theory of integration that is based on two axioms rather than on a construction involving Riemann sums. With several examples we demonstrate how to set up integrals in applications of calculus without using Riemann sums ...
Cavalcante, Ray, Todorov, Todor D.
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AIMS Mathematics, 2020 The derivation of integrals in the table of Gradshteyn and Ryzhik in terms of closed form solutions is always of interest. We evaluate several of these definite integrals of the form $\int_{0}^{\infty}\ln^k(\alpha y)\ln(R(y))dy$ in terms of a special ...
Robert Reynolds, Allan Stauffer
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Demonstratio Mathematica, 2022 In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals.
Kim Taekyun +3 more
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