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10 Bessel FunctionsBessel and Hankel Functions

§10.10 Continued Fractions

Assume Jν-1(z)0. Then

10.10.1 Jν(z)Jν-1(z)=12νz-1-12(ν+1)z-1-12(ν+2)z-1-,
z0,
10.10.2 Jν(z)Jν-1(z)=12z/ν1-14z2/(ν(ν+1))1-14z2/((ν+1)(ν+2))1-,
ν0,-1,-2,.

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