منابع مشابه
On two-dimensional Bessel functions
The general properties of two-dimensional generalized Bessel functions are discussed. Various asymptotic approximations are derived and applied to analyze the basic structure of the two-dimensional Bessel functions as well as their nodal lines.
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The Bessel-Muirhead hypergeometric system (or 0 F 1-system) in two variables (and three variables) is solved using symmetric series, with an explicit formula for coefficients , in order to express the K-Bessel function as a linear combination of the J-solutions. Limits of this method and suggestions for generalizations to a higher rank are discussed. 1. Introduction. The Bessel functions (of th...
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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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The consideration of tensor products of 0-Hecke algebra modules leads to natural analogs of the Bessel J-functions in the algebra of noncommutative symmetric functions. This provides a simple explanation of various combinatorial properties of Bessel functions.
متن کاملOn a Product of Modified Bessel Functions
Let Iν and Kν denote the modified Bessel functions of the first and second kinds of order ν. In this note we prove that the monotonicity of u → Iν(u)Kν(u) on (0,∞) for all ν ≥ −1/2 is an almost immediate consequence of the corresponding Turán type inequalities for the modified Bessel functions of the first and second kinds of order ν. Moreover, we show that the function u → Iν(u)Kν(u) is strict...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2006
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/39/48/008