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Elementary exact evaluation of infinite integrals of the product of several spherical Bessel functions, power and exponential. (English) Zbl 1276.33023

Summary: An elementary analytical method is presented for computation of integrals from zero to infinity involving the product of three 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 of them can be obtained from the function of zero order by an appropriate differentiation.

MSC:

33C55 Spherical harmonics
81V35 Nuclear physics
Full Text: DOI

References:

[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. · Zbl 1216.65033 · doi: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. · Zbl 0918.65002
[8] A. D. Jackson and L. C. Maximon, Integrals of products of Bessel functions, SIAM J. Math. Anal. 3 (1972), 446 – 460. · Zbl 0276.33019 · doi:10.1137/0503043
[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. · Zbl 0736.33004
[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. · Zbl 1221.33020 · doi: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. · Zbl 1369.33009 · doi:10.1109/TAP.2006.888467
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