Results 21 to 30 of about 1,846 (253)
MONOTONICITY AND CONVEXITY PROPERTIES OF THE NIELSEN’S β-FUNCTION
Проблемы анализа, 2017 The Nielsen’s β-function provides a powerful tool for evaluating and estimating certain integrals, series and mathematical constants. It is related to other special functions such as the digamma function, the Euler’s beta function and the Gauss ...
Kwara Nantomah
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Euler Type Integrals and Integrals in Terms of Extended Beta Function [PDF]
Journal of Mathematics, 2014 We derive the evaluations of certain integrals of Euler type involving generalized hypergeometric series. Further, we establish a theorem on extended beta function, which provides evaluation of certain integrals in terms of extended beta function and certain special polynomials.
Subuhi Khan, Mustafa Walid Al-Saad
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SMARANDACHE FUNCTION JOURNAL, 1 [PDF]
, 1990 This journal is yearly published (in the Spring or Fall) in a 300-400 pages volume, and 800-1000 copies. SNJ is a referred journal: reviewed, indexed, cited, concerning any of Smarandache type functions, numbers, sequences, integer algorithms, paradoxes,
Tabirca, Sabin, Tabirca, Tatiana
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Pendants to the Euler Beta function
, 2021 Motivated by the integral representation of the Euler Beta function, we introduce its Cauchy siblings and investigate some of their properties. Two of these newly introduced functions happen to coincide with some classical means, such as the arithmetic or the logarithmic Cauchy one. Although the bivariable generalizations of Beta functions are obtained
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Random division of an interval [PDF]
, 1967 The well-known relation between random division of an interval and the Poisson process is interpreted as a Laplace transformation.
BARTON D. E. +17 more
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Hacettepe Journal of Mathematics and Statistics, 2023 In the paper, by virtue of an integral representation of the Dirichlet beta function, with the aid of a relation between the Dirichlet beta function and the Euler numbers, and by means of a monotonicity rule for the ratio of two definite integrals with a parameter, the author finds increasing property and logarithmic convexity of two functions and two ...
Feng Qİ, Yong-hong YAO
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Successive approximations of $π$ using Euler Beta functions
, 2022 In this didactic note, we describe a procedure to derive successive approximations of $π$ using Euler Beta functions. It is an interesting exercise for undergraduate students, since it involves polynomial roots, integral calculations, inequalities and Euler Beta functions.
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Inverse hyperbolic equation, Spectral technique, Regularization method, Operational matrix
Kuwait Journal of ScienceRecently, the realm related to Euler's Beta function has played a significant role in the development of special function theory. In this study, a new extension of the special function known as Euler's Beta function with respect to the Mittag-Leffler ...
Firas Ghanim +2 more
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Recent Developments of Hilbert-Type Discrete and Integral Inequalities with Applications
International Journal of Mathematics and Mathematical Sciences, 2012 This paper deals with recent developments of Hilbert-type discrete and integral inequalities by introducing kernels, weight functions, and multiparameters.
Lokenath Debnath, Bicheng Yang
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On Some Generalizations of the Vandermonde Matrix and Their Relations with the Euler Beta-Function [PDF]
gmj, 1994 Abstract A multiple Vandermonde matrix which, besides the powers of variables, also contains their derivatives is introduced and an explicit expression of its determinant is obtained. For the case of arbitrary real powers, when the variables are positive, it is proved that such generalized multiple Vandermonde matrix is positive definite
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