§10.33 Continued Fractions

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

 10.33.1 $\frac{\mathop{I_{\nu}\/}\nolimits\!\left(z\right)}{\mathop{I_{\nu-1}\/}% \nolimits\!\left(z\right)}=\cfrac{1}{2\nu z^{-1}+}\cfrac{1}{2(\nu+1)z^{-1}+}% \cfrac{1}{2(\nu+2)z^{-1}+}\cdots,$ $z\neq 0$, Symbols: $\mathop{I_{\NVar{\nu}}\/}\nolimits\!\left(\NVar{z}\right)$: 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
 10.33.2 $\frac{\mathop{I_{\nu}\/}\nolimits\!\left(z\right)}{\mathop{I_{\nu-1}\/}% \nolimits\!\left(z\right)}=\cfrac{\frac{1}{2}z/\nu}{1+}\cfrac{\frac{1}{4}z^{2}% /(\nu(\nu+1))}{1+}\cfrac{\frac{1}{4}z^{2}/((\nu+1)(\nu+2))}{1+}\cdots,$ $\nu\neq 0,-1,-2,\ldots$. Symbols: $\mathop{I_{\NVar{\nu}}\/}\nolimits\!\left(\NVar{z}\right)$: 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