Digital Library of Mathematical Functions
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NIST
10 Bessel FunctionsSpherical Bessel Functions

§10.52 Limiting Forms

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§10.52(i) z0

§10.52(ii) z

10.52.3 jn(z) =z-1sin(z-12nπ)+|z|O(z-2),
yn(z) =-z-1cos(z-12nπ)+|z|O(z-2),
10.52.4 hn(1)(z) -n-1z-1z,
hn(2)(z) n+1z-1-z,
10.52.5 in(1)(z)in(2)(z)12z-1z,
|phz|12π-δ(<12π),
10.52.6 kn(z)12πz-1-z.