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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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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
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SIAM Review, 1967
Abstract : In the course of continuing investigations on the propagation of electromagnetic pulses, it became necessary to evaluate an integral involving exponential and Bessel functions. It was found that this integral had been evaluated incorrectly in the literature, and the error has been perpetuated for nearly 30 years.
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Abstract : In the course of continuing investigations on the propagation of electromagnetic pulses, it became necessary to evaluate an integral involving exponential and Bessel functions. It was found that this integral had been evaluated incorrectly in the literature, and the error has been perpetuated for nearly 30 years.
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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 ...
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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 coefficient of order zero occurred in 1732 in Daniel Bernoulli's memoir on the oscillations of ...
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Inequalities for the Zeros of Bessel Functions
SIAM Journal on Mathematical Analysis, 1977Let $j_{p,n} $, $j'_{p,n} $ denote the nth positive zeros of $J_p $, $J'_p $ respectively. It is shown that both $p^{ - 1} j_{p,n} $ and $p^{ - 1} j'_{p,n} $ are strictly decreasing functions of p.
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Exponentials and Bessel Functions
The Fibonacci Quarterly, 1976Davis, Bro. Basil, Hoggatt, V. E. jun.
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1998
We now turn to the solutions of the differential equations $$({{\Delta }_{{(q)}}} + \lambda )U = 0$$
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We now turn to the solutions of the differential equations $$({{\Delta }_{{(q)}}} + \lambda )U = 0$$
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New intregral transform with generalized Bessel–Maitland function kernel and its applications
Mathematical Methods in the Applied Sciences, 2021Durmuş Albayrak +2 more
exaly