§18.13 Continued Fractions

We use the terminology of §1.12(ii).

¶ Chebyshev

is the denominator of the th approximant to:

18.13.1

and is the denominator of the th approximant to:

18.13.2

¶ Legendre

is the denominator of the th approximant to:

18.13.3

where is an arbitrary nonzero constant.

¶ Laguerre

is the denominator of the th approximant to:

18.13.4

where is again an arbitrary nonzero constant.

¶ Hermite

is the denominator of the th approximant to:

18.13.5

See also Cuyt et al. (2008, pp. 91–99).