Elementary exact evaluation of infinite integrals of the product of several spherical Bessel functions, power and exponential
Author:
V. I. Fabrikant
Journal:
Quart. Appl. Math. 71 (2013), 573581
MSC (2000):
Primary 33C55, 81V35
Published electronically:
November 19, 2012
MathSciNet review:
3112829
Fulltext PDF
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Abstract: An elementary analytical method is presented for computation of integrals from zero to infinity involving the product of 3 or more spherical Bessel functions multiplied by an exponential and an arbitrary power. The method is based on the fact that spherical Bessel functions are essentially combinations of elementary functions and that any can be obtained from the function of zero order by an appropriate differentiation.
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 R. Anni and L. Taffara, DWBA analysis of heavy ion transfer reactions, Nuovo Cimento, 1974, Vol. A22, pp. 1124.
 2.
 N. Baddour, Operational and convolution properties of threedimensional Fourier transforms in spherical polar coordinates. Journal of Optical Society of America, Series A, 2010, Vol. 27, pp. 21442155.
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 J. Chen and J. Su, Glueball spectrum based on rigorous threedimensional relativistic equation for twogluon bound states II: calculation of glueball spectrum, Physics Reviews, 2004, Vol. D69, 076003.
 4.
 K.T.R Davies, Complexplane method for evaluating highly oscillatory integrals in nuclear physics, J. Phys. G: Nucl. Phys., 1988, Vol. 14, pp. 973994.
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 E. Elbaz, J. Meyer, and R. Nahabetian, On the expansion of a function sum of two vectors as appearing in the recoil effect in nuclear transfer reaction, Lett. Nuovo Cimento, 1974, Vol. 10, pp. 417421.
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 I.S. Gradshteyn and I.M. Ryzhik, Tables of Integrals, Series and Products. Academic Press Inc., New York, 1994. MR 1243179
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 A.D. Jackson and L. Maximon, Integrals of products of Bessel functions, SIAM J. Math. Anal., 1972, Vol. 3, pp. 446460. MR 0311958 (47:520)
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 ChengWei Qiu, LeWei Li, Saïd Zouhdi, TatSoon Teo, and Qun Wu, On the integral identities consisting of two spherical Bessel Functions. IEEE Transactions on Antennas and Propagation, Vol. 55, No. 1, pp. 240244. MR 2289746 (2008b:33012)
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Additional Information
V. I. Fabrikant
Affiliation:
Prisoner $#$167932D, Archambault Jail, 242 Montee Gagnon, SteAnneDesPlaines, Quebec, Canada J0N 1H0
Email:
valery{\textunderscore}fabrikant@hotmail.com
DOI:
http://dx.doi.org/10.1090/S0033569X2012013008
PII:
S 0033569X(2012)013008
Received by editor(s):
November 16, 2011
Published electronically:
November 19, 2012
Article copyright:
© Copyright 2012
Brown University
The copyright for this article reverts to public domain 28 years after publication.
