Some novel infinite series of spherical Bessel functions
Authors:
Andrew N. Vavreck and William Thompson Jr.
Journal:
Quart. Appl. Math. 42 (1984), 321-324
MSC:
Primary 33A40
DOI:
https://doi.org/10.1090/qam/757170
MathSciNet review:
757170
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Abstract: By a double application of the translational additional theorem for spherical wave functions, whereby one shifts an $n$ th order axisymmetric wave function from some origin to another and then in turn back to the first, one obtains a mathematical identity in the form of the $n$th order spherical wave function equated to an infinite series containing every order spherical wave function. The coefficients of the terms in this infinite series are themselves infinite series of spherical Bessel functions of arbitrary argument. These latter series must either sum to zero or unity to satisfy the mathematical identity. Following this reasoning, a collection of infinite series involving spherical Bessel functions has been generated. Some of the low mode order results are presented.
- Seymour Stein, Addition theorems for spherical wave functions, Quart. Appl. Math. 19 (1961), 15–24. MR 120407, DOI https://doi.org/10.1090/S0033-569X-1961-0120407-5
W. Thompson, Jr., Acoustic radiation and scattering from two eccentrically positioned spheres, Ph.D. dissertation, The Pennsylvania State University, 1971
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover Publications, New York 440, 1965
S. Stein, Addition theorems for spherical wave functions, Quart. Appl. Math. 19 15–24 (1961)
W. Thompson, Jr., Acoustic radiation and scattering from two eccentrically positioned spheres, Ph.D. dissertation, The Pennsylvania State University, 1971
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover Publications, New York 440, 1965
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Article copyright:
© Copyright 1984
American Mathematical Society