An Infinite Integral of Four Bessel Functions

SIAM Review ◽  
1993 ◽  
Vol 35 (2) ◽  
pp. 299-299
Author(s):  
M. L. Glasser
Keyword(s):  
Bessel Functions ◽  
Infinite Integral

A METHOD FOR THE DIRECT INTERPRETATION OF ELECTRICAL SOUNDINGS MADE OVER A FAULT OR DIKE

Geophysics ◽  
1973 ◽  
Vol 38 (4) ◽  
pp. 762-770 ◽  
Author(s):  
Terry Lee ◽  
Ronald Green
Keyword(s):  
Bessel Functions ◽  
Direct Analysis ◽  
Hankel Transform ◽  
Approximation Technique ◽  
Polarization Data ◽  
Resistivity Data ◽  
Vertical Fault ◽  
Direct Interpretation ◽  
Electrical Soundings ◽  
Infinite Integral

The potential function for a point electrode in the vicinity of a vertical fault or dike may be expressed as an infinite integral involving Bessel functions. Beginning with such an expression, two methods are presented for the direct analysis of resistivity data measured both normal and parallel to dikes or faults. The first method is based on the asymptotic expansion of the Hankel transform of the field data and is suitable for surveys done parallel to the strike of the dike or fault. The second method is based on a successive approximation technique which starts from an initial approximate solution and iterates until a solution with prescribed accuracy is found. Both methods are suitable for programming on a digital computer and some illustrative numerical results are presented. These examples show the limitations of the methods. In addition, the application of resistivity data to the interpretation of induced‐polarization data is pointed out.

An infinite integral involving Bessel functions and parabolic cylinder functions

1937 ◽  
Vol 33 (2) ◽  
pp. 210-211 ◽  
Author(s):  
R. S. Varma
Keyword(s):  
Bessel Functions ◽  
Parabolic Cylinder ◽  
Parabolic Cylinder Functions ◽  
Infinite Integral

The object of this paper is to evaluate an infinite integral involving Bessel functions and parabolic cylinder functions. The following two lemmas are required:Lemma 1. provided that R(m) > 0.

scholarly journals An Infinite Integral involving a Product of Two Modified Bessel Functions of the Second Kind

1953 ◽  
Vol 1 (4) ◽  
pp. 187-189 ◽  
Author(s):  
T. M. Macrobert
Keyword(s):  
Bessel Functions ◽  
Modified Bessel Functions ◽  
Infinite Integral ◽  
Image Position

The formula to be established iswhere l, m, n. are any numbers real or complex and R(b)>0. A similar result, involving Bessel Functions of the First Kind, was obtained by Hanumanta Rao [Mess, of Maths., XLVII. (1918), pp. 134–137].

An Infinite Integral of Four Bessel Functions (M. L. Glasser)

SIAM Review ◽  
1994 ◽  
Vol 36 (2) ◽  
pp. 285-287
Author(s):  
A. R. Miller
Keyword(s):  
Bessel Functions ◽  
Infinite Integral
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