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Rayleigh's Formulas

The formulas

j_n(z)=z^n(-1/zd/(dz))^n(sinz)/z
(1)
y_n(z)=-z^n(-1/zd/(dz))^n(cosz)/z
(2)

for n=0, 1, 2, ..., where j_n(z) is a spherical Bessel function of the first kind and y_n(z) is a spherical Bessel function of the second kind.

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References

Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 439, 1972.

Referenced on Wolfram|Alpha

Rayleigh's Formulas

Cite this as:

Weisstein, Eric W. "Rayleigh's Formulas." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RayleighsFormulas.html

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