Integrals Involving E-Functions and Modified Bessel Functions of the Second Kind
نویسندگان
چکیده
منابع مشابه
Some Integrals Involving Bessel Functions Some Integrals Involving Bessel Functions
A number of new definite integrals involving Bessel functions are presented. These have been derived by finding new integral representations for the product of two Bessel functions of different order and argument in terms of the generalized hypergeometric function with subsequent reduction to special cases. Connection is made with Weber's second exponential integral and Laplace transforms of pr...
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In this paper, we extend some known elementary trigonometric inequalities, and their hyperbolic analogues to Bessel and modified Bessel functions of the first kind. In order to prove our main results, we present some monotonicity and convexity properties of some functions involving Bessel and modified Bessel functions of the first kind. We also deduce some Turán and Lazarević-type inequalities ...
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Outline Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
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For ν an unrestricted real (or complex) number, let Iν be the modified Bessel function of the first kind of order ν, defined by [1, p. 77] Iν(x) = ∑ n≥0 (x/2)2n+ν n!0(ν + n+ 1) , which occurs frequently in problems of electrical engineering, finite elasticity, quantum billiards, wave mechanics, mathematical physics and chemistry, etc. Here x is an arbitrary real (or complex) number, and as usua...
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Some defin ite analytic integrals involving algebraic, trigonometric and Bessel functions which are needed in some electromagnetic calculations are proposed. The mathematical expansions are based on Mathematica (Wolfram) software and on some well known formulas. The agreement between the present expansion results and the numerical evaluation results is excellent.
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ژورنال
عنوان ژورنال: Proceedings of the Glasgow Mathematical Association
سال: 1954
ISSN: 2040-6185,2051-2104
DOI: 10.1017/s2040618500033001