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The term "continued fraction" is used to refer to a class of expressions of which generalized continued fraction of the form b_0+(a_1)/(b_1+(a_2)/(b_2+(a_3)/(b_3+...))) ...

The simple continued fraction representations of e given by [2; 1, 2, 1, 1, 4, 1, 1, 6, ...] (OEIS A003417). This continued fraction is sometimes known as Euler's continued ...

A simple continued fraction is a special case of a generalized continued fraction for which the partial numerators are equal to unity, i.e., a_n=1 for all n=1, 2, .... A ...

An algorithm for computing an Egyptian fraction, called the Farey sequence method by Bleicher (1972).

A rational number expressed in the form a/b (in-line notation) or a/b (traditional "display" notation), where a is called the numerator and b is called the denominator. When ...

Euler's continued fraction is the name given by Borwein et al. (2004, p. 30) to Euler's formula for the inverse tangent, ...

A periodic continued fraction is a continued fraction (generally a regular continued fraction) whose terms eventually repeat from some point onwards. The minimal number of ...

Gauss's continued fraction is given by the continued fraction ...

As Gauss showed in 1812, the hyperbolic tangent can be written using a continued fraction as tanhx=x/(1+(x^2)/(3+(x^2)/(5+...))) (Wall 1948, p. 349; Olds 1963, p. 138).

A generalized continued fraction is an expression of the form b_0+(a_1)/(b_1+(a_2)/(b_2+(a_3)/(b_3+...))), (1) where the partial numerators a_1,a_2,... and partial ...