analysis, a branch of mathematics, a generalized continued fraction is a generalization of regular continued fractions in canonical form, in which the partial...

expression is a generalized continued fraction. When it is necessary to distinguish the first form from generalized continued fractions, the former may...

In mathematics, an infinite periodic continued fraction is a continued fraction that can be placed in the form x = a 0 + 1 a 1 + 1 a 2 + 1 ⋱ a k + 1 a...

represent a convergent infinite continued fraction. This is written more compactly using generalized continued fraction notation: a 0 + a 0 a 1 + a 0 a...

60,17,\ldots ,4(4n-1),4n+1,\ldots ].} Here are some infinite generalized continued fraction expansions of e. The second is generated from the first by a...

Gauss's continued fraction is a particular class of continued fractions derived from hypergeometric functions. It was one of the first analytic continued fractions...

}}x^{2n}\\[8pt]\end{aligned}}} The sine function can also be represented as a generalized continued fraction: sin ⁡ ( x ) = x 1 + x 2 2 ⋅ 3 − x 2 + 2 ⋅ 3 x 2 4 ⋅ 5 − x 2...

truncated, with an ellipsis to show that they continue. Rational numbers have two continued fractions; the version in this list is the shorter one. Decimal...

{x}{x+2-{\cfrac {2x}{x+3-{\cfrac {3x}{x+4-\ddots }}}}}}}}} The following generalized continued fraction for ez converges more quickly: e z = 1 + 2 z 2 − z + z 2 6 +...

interest in generalized continued fractions and, following the work of John Wallis, he provided development in the generalized continued fraction of pi. This...