# §10.33 Continued Fractions

Assume $I_{\nu-1}\left(z\right)\neq 0$. Then

 10.33.1 $\frac{I_{\nu}\left(z\right)}{I_{\nu-1}\left(z\right)}=\cfrac{1}{2\nu z^{-1}+}% \cfrac{1}{2(\nu+1)z^{-1}+}\cfrac{1}{2(\nu+2)z^{-1}+}\cdots,$ $z\neq 0$, ⓘ Symbols: $I_{\NVar{\nu}}\left(\NVar{z}\right)$: modified Bessel function of the first kind, $z$: complex variable and $\nu$: complex parameter Referenced by: §10.74(v) Permalink: http://dlmf.nist.gov/10.33.E1 Encodings: TeX, pMML, png See also: Annotations for §10.33 and Ch.10
 10.33.2 $\frac{I_{\nu}\left(z\right)}{I_{\nu-1}\left(z\right)}=\cfrac{\frac{1}{2}z/\nu}% {1+}\cfrac{\frac{1}{4}z^{2}/(\nu(\nu+1))}{1+}\cfrac{\frac{1}{4}z^{2}/((\nu+1)(% \nu+2))}{1+}\cdots,$ $\nu\neq 0,-1,-2,\dotsc$. ⓘ Symbols: $I_{\NVar{\nu}}\left(\NVar{z}\right)$: modified Bessel function of the first kind, $z$: complex variable and $\nu$: complex parameter Referenced by: §10.74(v) Permalink: http://dlmf.nist.gov/10.33.E2 Encodings: TeX, pMML, png See also: Annotations for §10.33 and Ch.10