Some Bessel function expansions

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...

Some Distributions Involving Bessel Functions

Bessel Function Zeroes

0  1  2  3   as does its derivative  0 (): 0  0 1   0 2   0 3     0 0 = 0 01   0 02   0 03   0 04    = 0 See Tables 1 & 2 for the cases  = 0 1 2 and Tables 3 & 4 for the cases  = 12 32 52. These appear in many physical applications that we cannot hope to survey in entirety. We will state only a few properties and several importan...

A Bessel Function Multiplier

We obtain nearly sharp estimates for the L p (R 2) norms of certain convolution operators. For n 1 let n be the measure on R 2 obtained by multiplying normalized arclength measure on fjxj = 1g by the oscillating factor e inarg(x). For 1 p 1, let C(p; n) denoted the norm of the operator T n f : = n f on L p (R 2). The purpose of this note is to estimate the rate of decay of C(p; n) as n ! 1. By ...

Transplantation and Multiplier Theorems for Fourier-bessel Expansions

Proved are weighted transplantation inequalities for Fourier-Bessel expansions. These extend known results on this subject by considering the largest possible range of parameters, allowing more weights and admitting a shift. The results are then used to produce a fairly general multiplier theorem with power weights for considered expansions. Also fractional integral results and conjugate functi...