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Physical Mathematics, 2019
The subject of Bessel functions is an old one. The earliest mention of these functions was dated October 3, 1703, when a series now described as a Bessel function of order 1/3 appeared in a letter from Jakob Bernoulli to Leibniz [(13) p. 356]. The Bessel
Julian Schwinger +3 more
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The subject of Bessel functions is an old one. The earliest mention of these functions was dated October 3, 1703, when a series now described as a Bessel function of order 1/3 appeared in a letter from Jakob Bernoulli to Leibniz [(13) p. 356]. The Bessel
Julian Schwinger +3 more
semanticscholar +5 more sources
, 2023 The subject of Bessel functions is an old one. The earliest mention of these functions was dated October 3, 1703, when a series now described as a Bessel function of order 1/3 appeared in a letter from Jakob Bernoulli to Leibniz [(13) p. 356]. The Bessel coefficient of order zero occurred in 1732 in Daniel Bernoulli's memoir on the oscillations of ...
Funk, Louis J.
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Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales - Serie A: Matematicas, 2020
Yuming Chu +2 more
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Yuming Chu +2 more
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Bessel Functions of the First Kind
Bounded Gaps Between Primes, 2021Bessel Functions of the First Kind • Recall the Bessel equation x2y′′ + xy′ + (x − n)y = 0. • For a fixed value of n, this equation has two linearly independent solutions.
K. Broughan
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Jordan type inequalities involving the Bessel and modified Bessel functions [PDF]
Computers and Mathematics With Applications, 2010 In this work, two general forms of Jordan’s inequalities for the Bessel and modified Bessel functions are established, and proved by using l’Hospital’s rule for monotonicity and some properties of the spherical Bessel and the modified spherical Bessel ...
Ling Zhu
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Higher derivatives of the Bessel functions with respect to the order
Integral Transforms and Special Functions, 2016Yu A Brychkov
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Sampling bessel functions and bessel sampling
2013 IEEE 8th International Symposium on Applied Computational Intelligence and Informatics (SACI), 2013The main aim of this article is to establish summation formulae in form of sampling expansion series for Bessel functions , and , and obtain sharp truncation error upper bounds occurring in the –Bessel sampling series approximation. The principal derivation tools are the famous sampling theorem by Kramer and various properties of Bessel and modified ...
Dragana Jankov Masirevic +3 more
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Applicable Algebra in Engineering, Communication and Computing, 1992
The authors present a linear combination of two integrals for calculating the integral \[ \int^ \infty_ 0xe^{-\eta x^ 2}J_ b(Kx)Y_ b(kx)dx \] where \(\eta\), \(K\), \(k\) and \(b\) are all positive real numbers. Bessel functions and Shkarofsky functions are used for this transformation.
Ross C. McPhedran +2 more
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The authors present a linear combination of two integrals for calculating the integral \[ \int^ \infty_ 0xe^{-\eta x^ 2}J_ b(Kx)Y_ b(kx)dx \] where \(\eta\), \(K\), \(k\) and \(b\) are all positive real numbers. Bessel functions and Shkarofsky functions are used for this transformation.
Ross C. McPhedran +2 more
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, 1999 This thesis is consists of four chapters. In the first chapter, Bessel equation is obtained through the cylindrical coordinates of Laplace equation. In addition, Bessel functions which are the solutions of Bessel equation and their properties are studied.
Uygun, Nihan
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Journal of Mathematical Physics, 2003
A formula for the Taylor series expansion of the rth power of the modified Bessel function [Iν(z)]r is derived for arbitrary r. The result is expressed in terms of a recursive formula for a class of polynomials, which facilitates the systematic construction of the expansion of [Iν(z)]r.
Bender, Carl M. +2 more
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A formula for the Taylor series expansion of the rth power of the modified Bessel function [Iν(z)]r is derived for arbitrary r. The result is expressed in terms of a recursive formula for a class of polynomials, which facilitates the systematic construction of the expansion of [Iν(z)]r.
Bender, Carl M. +2 more
openaire +2 more sources