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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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.
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In particular we shall first determine a radius of univalence for the normalized Bessel functions [7>(z)]1/" for values of v belonging to the region G defined by the inequalities 6{\v} >0, | arg »»| <7r/4. Then we shall determine the radius of univalence of the functions z1_"7,.(z) for values of v belonging to a subset of the closure of G. When v is real and positive we shall determine the exac...
متن کاملGeneralized Bessel functions for p-radial functions
Suppose that d ∈ N and p > 0. In this paper, we study the generalized Bessel functions for the surface {v ∈ Rd : |v|p = 1}, introduced by D.St.P. Richards. We derive a recurrence relation for these functions and utilize a series representation to relate them to the classical symmetric functions. These generalized Bessel functions are symmetric with respect to the action of the hyperoctahedral g...
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A polynomial approximation to Bessel functions that arises from an electromagnetic scattering problem is examined. The approximation is extended to Bessel functions of any integer order, and the relationship to the Taylor series is derived. Numerical calculations show that the polynomial approximation and the Taylor series truncated to the same order have similar accuracies.
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ژورنال
عنوان ژورنال: Nature
سال: 1938
ISSN: 0028-0836,1476-4687
DOI: 10.1038/142934a0