Zobrazeno 1 - 10
of 223
pro vyhledávání: '"Catalan's constant"'
Autor:
Yulei Chen, Dongwei Guo
Publikováno v:
Axioms, Vol 13, Iss 4, p 230 (2024)
Making use of integration by parts and variable replacement methods, we derive some interesting explicit definite integral formulae involving trigonometric or hyperbolic functions, whose results are expressed in terms of Catalan’s constant, Dirichl
Externí odkaz:
https://doaj.org/article/6e1f4e02d25d4c37a55cbc35bfdce27f
Autor:
Chunli Li, Wenchang Chu
Publikováno v:
Mathematics, Vol 12, Iss 4, p 589 (2024)
Eight infinite series involving harmonic-like numbers are coherently and systematically reviewed. They are evaluated in closed form exclusively by integration together with calculus and complex analysis. In particular, a mysterious series W is introd
Externí odkaz:
https://doaj.org/article/4f9c44a82b18476b93984ee9a0eceebe
Akademický článek
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Autor:
Robert Reynolds, Allan Stauffer
Publikováno v:
AIMS Mathematics, Vol 7, Iss 10, Pp 18576-18586 (2022)
A Prudnikov sum is extended to derive the finite sum of the Hurwitz-Lerch Zeta function in terms of the Hurwitz-Lerch Zeta function. This formula is then used to evaluate a number trigonometric sums and products in terms of other trigonometric functi
Externí odkaz:
https://doaj.org/article/b1615d2c0db140a6bda71083d088cd1e
Autor:
Robert Reynolds, Allan Stauffer
Publikováno v:
Ural Mathematical Journal, Vol 8, Iss 2 (2022)
With a possible connection to integrals used in General Relativity, we used our contour integral method to write a closed form solution for a quadruple integral involving exponential functions and logarithm of quotient radicals. Almost all Hurwitz–
Externí odkaz:
https://doaj.org/article/e136bced4ec44f1a851b3ea79d298baf
Akademický článek
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Autor:
Robert Reynolds, Allan Stauffer
Publikováno v:
AIMS Mathematics, Vol 5, Iss 6, Pp 7252-7258 (2020)
In this paper by means of contour integration we will evaluate definite integrals of the form \begin{equation*} \int_{0}^{1}\left(\ln^k(ay)-\ln^k\left(\frac{a}{y}\right)\right)R(y)dy \end{equation*} in terms of a special function, where $R(y)$ is a g
Externí odkaz:
https://doaj.org/article/0959a11bdccb4547a39dd2a4ef011030
Publikováno v:
Қарағанды университетінің хабаршысы. Математика сериясы, Vol 103, Iss 3 (2021)
In this article we obtain the summations of some infinite series by partial fraction method and by using certain hypergeometric summation theorems of positive and negative unit arguments, Riemann Zeta functions, polygamma functions, lower case beta f
Externí odkaz:
https://doaj.org/article/c80a5ee008d44e47925856f27a460e20
Publikováno v:
Symmetry, Vol 14, Iss 12, p 2502 (2022)
Due to the great success of hypergeometric functions of one variable, a number of hypergeometric functions of two or more variables have been introduced and explored. Among them, the Kampé de Fériet function and its generalizations have been active
Externí odkaz:
https://doaj.org/article/8b8918988e4a413dac3ed6c7aefd82ed
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