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10 Bessel FunctionsModified Bessel Functions

§10.30 Limiting Forms

Contents

§10.30(i) z0

When ν is fixed and z0,

10.30.1 Iν(z)(12z)ν/Γ(ν+1),
ν-1,-2,-3,,
10.30.2 Kν(z) 12Γ(ν)(12z)-ν,
ν>0,
10.30.3 K0(z) -lnz.

For Kν(x), when ν is purely imaginary and x0+, see (10.45.2) and (10.45.7).

§10.30(ii) z

When ν is fixed and z,

10.30.4 Iν(z) ez/2πz,
|phz|12π-δ,
10.30.5 Iν(z) e±(ν+12)πie-z/2πz,
12π+δ±phz32π-δ.

For Kν(z) see (10.25.3).