Results 1 to 10 of about 80 (79)
Series acceleration formulas obtained from experimentally discovered hypergeometric recursions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2023 In 2010, Kh. Hessami Pilehrood and T. Hessami Pilehrood introduced generating function identities used to obtain series accelerations for values of Dirichlet's $\beta$ function, via the Markov--Wilf--Zeilberger method.
Paul Levrie, John Campbell
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Is Catalan’s Constant Rational?
Mathematics, 2022 This paper employs a contour integral method to derive and evaluate the infinite sum of the Euler polynomial expressed in terms of the Hurwitz Zeta function. We provide formulae for several classes of infinite sums of the Euler polynomial in terms of the
Robert Reynolds, Allan Stauffer
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Axioms, 2021 In this paper, we have derived and evaluated a quadruple integral whose kernel involves the logarithm and product of Bessel functions of the first kind. A new quadruple integral representation of Catalan’s G and Apéry’s ζ(3) constants are produced.
Robert Reynolds, Allan Stauffer
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Evaluation of Infinite Series by Integrals
Mathematics, 2022 We examine a large class of infinite triple series and establish a general summation formula. This is done by expressing the triple series in terms of definite integrals involving arctangent function that are evaluated in turn in closed forms.
Chunli Li, Wenchang Chu
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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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Series acceleration formulas for beta values [PDF]
Discrete Mathematics & Theoretical Computer Science, 2010 We prove generating function identities producing fast convergent series for the sequences beta(2n + 1); beta(2n + 2) and beta(2n + 3), where beta is Dirichlet's beta function.
Khodabakhsh Hessami Pilehrood +1 more
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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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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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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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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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