Some special functions and cylindrical diffusion equation on α-time scale
Demonstratio MathematicaThis article is dedicated to present various concepts on α\alpha -time scale, including power series, Taylor series, binomial series, exponential function, gamma function, and Bessel functions of the first kind.
Silindir Burcu +3 more
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Integral Representations of Generalized Mathieu Series Via Mittag-Leffler Type Functions [PDF]
, 2007 Mathematics Subject Classification: 33C05, 33C10, 33C20, 33C60, 33E12, 33E20, 40A30The main purpose of this paper is to present a number of potentially useful integral representations for the generalized Mathieu series as well as for its alternating ...
Tomovski, Živorad
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Inequalities for integrals of the modified Struve function of the first kind
, 2018 Simple inequalities for some integrals involving the modified Struve function of the first kind $\mathbf{L}_{\nu}(x)$ are established. In most cases, these inequalities have best possible constant.
Gaunt, Robert E.
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A note on the asymptotics of the modified Bessel functions on the Stokes lines [PDF]
, 2017 We employ the exponentially improved asymptotic expansions of the confluent hypergeometric functions on the Stokes lines discussed by the author [Appl. Math. Sci. 7 (2013) 6601–6609] to give the analogous expansions of the modified Bessel functions Iν(z)
Paris, R. B.
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Asymptotic expansions relating to the distribution of the length of longest increasing subsequences
Forum of Mathematics, SigmaWe study the distribution of the length of longest increasing subsequences in random permutations of n integers as n grows large and establish an asymptotic expansion in powers of $n^{-1/3}$ .
Folkmar Bornemann
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The evaluation of a definite integral by the method of brackets illustrating its flexibility
Open MathematicsThe method of brackets is a procedure to evaluate definite integrals over a half-line. It consists of a small number of rules. This article illustrates the method by evaluating an integral by several variations of the method. The integrand is the product
Gonzalez Ivan +2 more
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On Hankel Transform of Generalized Mathieu Series [PDF]
, 2009 Mathematics Subject Classification: Primary 33E20, 44A10; Secondary 33C10, 33C20, 44A20By using integral representations for several Mathieu type series, a number of integral transforms of Hankel type are derived here for general families of Mathieu ...
Tomovski, Živorad
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The radius of convexity of normalized Bessel functions
, 2015 The radius of convexity of two normalized Bessel functions of the first kind are determined in the case when the order is between $-2$ and $-1.$ Our methods include the minimum principle for harmonic functions, the Hadamard factorization of some Dini ...
Baricz, Árpád, Szász, Róbert
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Generalization of the Modified Bessel Function and Its Generating Function [PDF]
, 2005 2000 Mathematics Subject Classification: 33C10, 33-02, 60K25This paper presents new generalizations of the modified Bessel function and its generating function.
Griffiths, J. +2 more
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The evaluation of single Bessel function sums [PDF]
, 2018 We examine convergent representations for the sums of Bessel functions X∞ n=1 Jν(nx) nα (x > 0) and X∞ n=1 Kν(nz) nα (<(z) > 0), together with their alternating versions, by a Mellin transform approach.
Paris, R. B.
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