Zobrazeno 1 - 10
of 217
pro vyhledávání: '"Apéry's constant"'
Autor:
Robert Reynolds, Allan Stauffer
Publikováno v:
Mathematics, Vol 10, Iss 22, p 4251 (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
Externí odkaz:
https://doaj.org/article/aa49d60a35cf4b06aa710b99e30b8f1d
Autor:
Robert Reynolds, Allan Stauffer
Publikováno v:
Symmetry, Vol 14, Iss 8, p 1573 (2022)
A new three-dimensional integral containing f(x,y,z)Iv(xα) is derived where Iv(xα) is the Modified Bessel Function of the first kind and the integral is taken over the infinite cubic space 0
Externí odkaz:
https://doaj.org/article/28c6e3f86dc3428b87a2c2bc05a3e106
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Autor:
Robert Reynolds, Allan Stauffer
Publikováno v:
Symmetry, Vol 14, Iss 2, p 205 (2022)
A four-dimensional integral containing g(x,y,z,t)Cn(λ)(x) is derived. Cn(λ)(x) is the Gegenbauer polynomial, g(x,y,z,t) is a product of the generalized logarithm quotient functions and the integral is taken over the region 0≤x≤1,0≤y≤1,0≤z
Externí odkaz:
https://doaj.org/article/94ba0486f6ae4687a1bfce0159b242de
Autor:
Robert Reynolds, Allan Stauffer
Publikováno v:
Symmetry, Vol 14, Iss 1, p 100 (2022)
The aim of the current document is to evaluate a quadruple integral involving the Chebyshev polynomial of the first kind Tn(x) and derive in terms of the Hurwitz-Lerch zeta function. Special cases are evaluated in terms of fundamental constants. The
Externí odkaz:
https://doaj.org/article/2a85e5f8da264e109df97da3ab9ef02f
Autor:
Robert Reynolds, Allan Stauffer
Publikováno v:
Symmetry, Vol 14, Iss 1, p 9 (2021)
The objective of the present paper is to obtain a quadruple infinite integral. This integral involves the product of the Struve and parabolic cylinder functions and expresses it in terms of the Hurwitz–Lerch Zeta function. Almost all Hurwitz-Lerch
Externí odkaz:
https://doaj.org/article/ce73486247c7402abc9664f5b71ab163
Autor:
Robert Reynolds, Allan Stauffer
Publikováno v:
Symmetry, Vol 13, Iss 11, p 2056 (2021)
A closed form expression for a triple integral not previously considered is derived, in terms of the Lerch function. Almost all Lerch functions have an asymmetrical zero-distribution. The kernel of the integral involves the product of the logarithmic
Externí odkaz:
https://doaj.org/article/1b45877391ec427ea15f394a1629be0d
Autor:
Robert Reynolds, Allan Stauffer
Publikováno v:
Axioms, Vol 10, Iss 4, p 279 (2021)
We derive a new formula for the Hurwitz–Lerch zeta function in terms of the infinite sum of the incomplete gamma function. Special cases are derived in terms of fundamental constants.
Externí odkaz:
https://doaj.org/article/31e9b513b1aa4b918d915f4f7dbcb1de
Publikováno v:
Mathematical Modelling and Analysis, Vol 24, Iss 3 (2019)
We show that integrals involving the log-tangent function, with respect to any square-integrable function on , can be evaluated by the harmonic series. Consequently, several formulas and algebraic properties of the Riemann zeta function at odd positi
Externí odkaz:
https://doaj.org/article/6ff99c35f212497380bb8f590cf1a43e
Autor:
Zhi-Hong Sun
Publikováno v:
AIMS Mathematics, Vol 7, Iss 2, Pp 2729-2781 (2022)
Let $ \{S_n\} $ be the Apéry-like sequence given by $ S_n = \sum_{k = 0}^n\binom nk\binom{2k}k\binom{2n-2k}{n-k} $. We show that for any odd prime $ p $, $ \sum_{n = 1}^{p-1}\frac {nS_n}{8^n}{\equiv} (1-(-1)^{\frac{p-1}2})p^2\ (\text{ mod}\ {p^3}) $
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::abc62e2604e4db1ff8c844ea302a4786
https://doi.org/10.3934/math.2022153
https://doi.org/10.3934/math.2022153