# §18.13 Continued Fractions

We use the terminology of §1.12(ii).

## Chebyshev

$\mathop{T_{n}\/}\nolimits\!\left(x\right)$ is the denominator of the $n$th approximant to:

 18.13.1 $\cfrac{-1}{x+\cfrac{-1}{2x+\cfrac{-1}{2x+}}}\cdots,$ Symbols: $x$: real variable Permalink: http://dlmf.nist.gov/18.13.E1 Encodings: TeX, pMML, png See also: Annotations for 18.13

and $\mathop{U_{n}\/}\nolimits\!\left(x\right)$ is the denominator of the $n$th approximant to:

 18.13.2 $\cfrac{-1}{2x+\cfrac{-1}{2x+\cfrac{-1}{2x+}}}\cdots.$ Symbols: $x$: real variable Permalink: http://dlmf.nist.gov/18.13.E2 Encodings: TeX, pMML, png See also: Annotations for 18.13

## Legendre

$\mathop{P_{n}\/}\nolimits\!\left(x\right)$ is the denominator of the $n$th approximant to:

 18.13.3 $\cfrac{a_{1}}{x+\cfrac{-\frac{1}{2}}{\frac{3}{2}x+\cfrac{-\frac{2}{3}}{\frac{5% }{3}x+\cfrac{-\frac{3}{4}}{\frac{7}{4}x+}}}}\cdots,$ Symbols: $x$: real variable Permalink: http://dlmf.nist.gov/18.13.E3 Encodings: TeX, pMML, png See also: Annotations for 18.13

where $a_{1}$ is an arbitrary nonzero constant.

## Laguerre

$\mathop{L_{n}\/}\nolimits\!\left(x\right)$ is the denominator of the $n$th approximant to:

 18.13.4 $\cfrac{a_{1}}{1-x+\cfrac{-\frac{1}{2}}{\frac{1}{2}(3-x)+\cfrac{-\frac{2}{3}}{% \frac{1}{3}(5-x)+\cfrac{-\frac{3}{4}}{\frac{1}{4}(7-x)+}}}}\cdots,$ Symbols: $x$: real variable Permalink: http://dlmf.nist.gov/18.13.E4 Encodings: TeX, pMML, png See also: Annotations for 18.13

where $a_{1}$ is again an arbitrary nonzero constant.

## Hermite

$\mathop{H_{n}\/}\nolimits\!\left(x\right)$ is the denominator of the $n$th approximant to:

 18.13.5 $\cfrac{1}{2x+\cfrac{-2}{2x+\cfrac{-4}{2x+\cfrac{-6}{2x+}}}}\cdots.$ Symbols: $x$: real variable Permalink: http://dlmf.nist.gov/18.13.E5 Encodings: TeX, pMML, png See also: Annotations for 18.13