unmodified functions

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1: 10.51 Recurrence Relations and Derivatives

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§10.51(i) Unmodified Functions

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2: 10.49 Explicit Formulas

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§10.49(i) Unmodified Functions

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10.49.7 $${𝗁}_n^{(2)}\left(z\right)={\mathrm{e}}^{-\mathrm{i}z}\sum _{k=0}^n{(-\mathrm{i})}^{k-n-1}\frac{a_k(n+\frac{1}{2})}{z^{k+1}}.$$

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Symbols:

$\mathrm{e}$: base of natural logarithm, $\mathrm{i}$: imaginary unit, ${𝗁}_n^{(2)}\left(z\right)$: spherical Bessel function of the third kind, $n$: integer, $k$: nonnegative integer, $z$: complex variable and $a_k(\nu )$: polynomial coefficient

A&S Ref:

10.1.17 (corrected)

Permalink:

http://dlmf.nist.gov/10.49.E7

Encodings:

pMML, png, TeX

See also:

Annotations for §10.49(i), §10.49 and Ch.10

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3: 10.43 Integrals

… ►For infinite integrals of triple products of modified and unmodified Bessel functions, see Gervois and Navelet (1984, 1985a, 1985b, 1986a, 1986b). …