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Date: 17-6-2019
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Date: 17-9-2018
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Date: 27-8-2019
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The spherical Bessel function of the second kind, denoted or , is defined by
(1) |
where is a Bessel function of the second kind and, in general, and are complex numbers.
The spherical Bessel function of the second kind is implemented in the Wolfram Language as SphericalBesselY[n,z].
The function is most commonly encountered in the case an integer, in which case it is given by
(2) |
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(3) |
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(4) |
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(5) |
where is a Bessel function of the first kind.
Specific cases for small nonnegative are given by
(6) |
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(7) |
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(8) |
REFERENCES:
Abramowitz, M. and Stegun, I. A. (Eds.). "Spherical Bessel Functions." §10.1 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 437-442, 1972.
Arfken, G. "Spherical Bessel Functions." §11.7 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 622-636, 1985.
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