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10 Bessel FunctionsBessel and Hankel Functions

§10.10 Continued Fractions

Assume Jν1(z)0. Then

10.10.1 Jν(z)Jν1(z)=12νz112(ν+1)z112(ν+2)z1,
z0,
10.10.2 Jν(z)Jν1(z)=12z/ν114z2/(ν(ν+1))114z2/((ν+1)(ν+2))1,
ν0,1,2,.

See also Cuyt et al. (2008, pp. 349–356).