Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
  Quarterly of Applied Mathematics
Quarterly of Applied Mathematics
  
Online ISSN 1552-4485; Print ISSN 0033-569X
 

   

 

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), 573-581
MSC (2000): Primary 33C55, 81V35
Published electronically: November 19, 2012
MathSciNet review: 3112829
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • 1. R. Anni and L. Taffara, DWBA analysis of heavy ion transfer reactions, Nuovo Cimento, 1974, Vol. A22, pp. 11-24.
  • 2. N. Baddour, Operational and convolution properties of three-dimensional Fourier transforms in spherical polar coordinates. Journal of Optical Society of America, Series A, 2010, Vol. 27, pp. 2144-2155.
  • 3. J. Chen and J. Su, Glueball spectrum based on rigorous three-dimensional relativistic equation for two-gluon bound states II: calculation of glueball spectrum, Physics Reviews, 2004, Vol. D69, 076003.
  • 4. K.T.R Davies, Complex-plane method for evaluating highly oscillatory integrals in nuclear physics, J. Phys. G: Nucl. Phys., 1988, Vol. 14, pp. 973-994.
  • 5. 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. 417-421.
  • 6. B. Gebremariam, T. Duguet, and S. K. Bogner, Symbolic integration of a product of two spherical Bessel functions with an additional exponential and polynomial factor, Comput. Phys. Comm. 181 (2010), no. 6, 1136–1143. MR 2644952, 10.1016/j.cpc.2010.02.006
  • 7. I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, 5th ed., Academic Press, Inc., Boston, MA, 1994. Translation edited and with a preface by Alan Jeffrey. MR 1243179 (94g:00008)
  • 8. A. D. Jackson and L. C. Maximon, Integrals of products of Bessel functions, SIAM J. Math. Anal. 3 (1972), 446–460. MR 0311958 (47 #520)
  • 9. R. Mehrem, J. T. Londergan, and M. H. Macfarlane, Analytic expressions for integrals of products of spherical Bessel functions, J. Phys. A 24 (1991), no. 7, 1435–1453. MR 1121820 (92h:33011)
  • 10. R. Mehrem and A. Hohenegger, A generalization for the infinite integral over three spherical Bessel functions, J. Phys. A 43 (2010), no. 45, 455204, 9. MR 2733847 (2011k:33012), 10.1088/1751-8113/43/45/455204
  • 11. Cheng-Wei Qiu, Le-Wei Li, Saïd Zouhdi, Tat-Soon Yeo, and Qun Wu, On the integral identities consisting of two spherical Bessel functions, IEEE Trans. Antennas and Propagation 55 (2007), no. 1, 240–244. MR 2289746 (2008b:33012), 10.1109/TAP.2006.888467

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC (2000): 33C55, 81V35

Retrieve articles in all journals with MSC (2000): 33C55, 81V35


Additional Information

V. I. Fabrikant
Affiliation: Prisoner $#$167932D, Archambault Jail, 242 Montee Gagnon, Ste-Anne-Des-Plaines, Quebec, Canada J0N 1H0
Email: valery{\textunderscore}fabrikant@hotmail.com

DOI: http://dx.doi.org/10.1090/S0033-569X-2012-01300-8
PII: S 0033-569X(2012)01300-8
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.



Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2015 Brown University
Comments: qam-query@ams.org
AMS Website