# §10.10 Continued Fractions

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

 10.10.1 $\frac{\mathop{J_{\nu}\/}\nolimits\!\left(z\right)}{\mathop{J_{\nu-1}\/}% \nolimits\!\left(z\right)}=\cfrac{1}{2\nu z^{-1}-\cfrac{1}{2(\nu+1)z^{-1}-% \cfrac{1}{2(\nu+2)z^{-1}-\cdots}}},$ $z\neq 0$, Symbols: $\mathop{J_{\NVar{\nu}}\/}\nolimits\!\left(\NVar{z}\right)$: Bessel function of the first kind, $z$: complex variable and $\nu$: complex parameter A&S Ref: 9.1.73 Referenced by: §10.33, §10.74(v) Permalink: http://dlmf.nist.gov/10.10.E1 Encodings: TeX, pMML, png See also: Annotations for 10.10
 10.10.2 $\frac{\mathop{J_{\nu}\/}\nolimits\!\left(z\right)}{\mathop{J_{\nu-1}\/}% \nolimits\!\left(z\right)}=\cfrac{\tfrac{1}{2}z/\nu}{1-\cfrac{\tfrac{1}{4}z^{2% }/(\nu(\nu+1))}{1-\cfrac{\tfrac{1}{4}z^{2}/((\nu+1)(\nu+2))}{1-\cdots}}},$ $\nu\neq 0,-1,-2,\ldots$. Symbols: $\mathop{J_{\NVar{\nu}}\/}\nolimits\!\left(\NVar{z}\right)$: Bessel function of the first kind, $z$: complex variable and $\nu$: complex parameter A&S Ref: 9.1.73 Referenced by: §10.33, §10.74(v) Permalink: http://dlmf.nist.gov/10.10.E2 Encodings: TeX, pMML, png See also: Annotations for 10.10