Results 11 to 20 of about 302 (59)
Efficient estimate of the remainder for the Dirichlet function η(p) for p ∈ R+ [PDF]
, 2020 For any k,n,q ∈N, where n≥ 2k+1≥ 3, and p ∈R+ the nth remainder ρ(n, p) of the Dirichlet eta function η(p), known also as the alternating Riemann zeta function, η(p) := ∞ ∑ i=1 (−1)i+1 1 ip , is given in the form ρ(n, p) = ∆q(n, p)+δq(k, p), where k and ...
Lampret, V.
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Approximations related to the complete p-elliptic integrals
Open Mathematics, 2022 In this paper, the authors present some monotonicity properties for certain functions involving the complete p-elliptic integrals of the first and second kinds, by showing the monotonicity and concavity-convexity properties of certain combinations ...
Zhong Genhong, Ma Xiaoyan, Wang Fei
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Asymptotic evaluation of $\int_0^\infty\left(\frac{\sin x}{x}\right)^n\;dx$ [PDF]
Commun. Korean Math. Soc. 35 (2020), 1193-1202, 2020 We consider the integral $\int_0^\infty\left(\frac{\sin x}{x}\right)^n\;dx$ as a function of the positive integer $n$. We show that there exists an asymptotic series in $\frac{1}{n}$ and compute the first terms of this series together with an explicit error bound.
arxiv +1 more source
Open Mathematics, 2019 In this work, we propose to approximate the Gaussian integral, the error function and the cumulative distribution function by using the power series extender method (PSEM).
Sandoval-Hernandez Mario A. +3 more
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Symbolic Evaluation of Coefficients in Airy-type Asymptotic Expansions [PDF]
J. Math. Analysis and Appl., 269(2002), pp 317-331, 2001 Computer algebra algorithms are developed for evaluating the coefficients in Airy-type asymptotic expansions that are obtained from integrals with a large parameter. The coefficients are defined from recursive schemes obtained from integration by parts. An application is given for the Weber parabolic cylinder function.
arxiv +1 more source
The agreement between novel exact and numerical solutions of nonlinear models
Partial Differential Equations in Applied Mathematics, 2023 Nonlinear models (NLMs), being an important topic in mathematical physics, have attracted a lot of attention in the international research community because they have numerous uses in human life. These NLMs are typically implemented to illuminate various
Md. Nur Alam, S. M. Rayhanul Islam
doaj
Ramanujan Theta Function Identities and Quadratic Numbers [PDF]
arXiv, 2023 Eigenvectors of the discrete Fourier transform can be expressed using Ramanujan theta functions. New theta function identities, Ramanujan theta function identities, and generating functions for the quadratic numbers are a consequence.
arxiv
Alexandria Engineering Journal, 2020 In this research, analytical and numerical solutions are studied of a two–dimensional discrete electrical lattice, which is mathematically represented by the modified Zakharov–Kuznetsov equation.
Choonkil Park +4 more
doaj
Comparison of methods for the calculation of the real dilogarithm regarding instruction-level parallelism [PDF]
arXiv, 2022 We compare different methods for the computation of the real dilogarithm regarding their ability for using instruction-level parallelism when executed on appropriate CPUs. As a result we present an instruction-level-aware method and compare it to existing implementations.
arxiv
Demonstratio MathematicaIn this work, we present a sophisticated operating algorithm, the reproducing kernel Hilbert space method, to investigate the approximate numerical solutions for a specific class of fractional Begley-Torvik equations (FBTE) equipped with fractional ...
Aljazzazi Mazin +4 more
doaj +1 more source