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10 Bessel FunctionsModified Bessel Functions

§10.33 Continued Fractions

Assume Iν1(z)0. Then

10.33.1 Iν(z)Iν1(z)=12νz1+12(ν+1)z1+12(ν+2)z1+,
z0,
10.33.2 Iν(z)Iν1(z)=12z/ν1+14z2/(ν(ν+1))1+14z2/((ν+1)(ν+2))1+,
ν0,1,2,.

See also Cuyt et al. (2008, pp. 361–367).