Simplifying an infinite fraction

Asked Jun 01 '18 at 16:02

Active Jun 01 '18 at 17:04

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I am unfamiliar with infinite fractions and are far more comfortable working with infinite sums, products, etc. Is there a way to convert this function which takes the form of an infinite fraction into an algebraic form or infinite sum/product so that it can be more easily evaluated?

$f\left( x \right) =x+\frac { 1 }{ 1+x+\frac { 1 }{ 2+x+\frac { 1 }{ 3+x+\frac { 1 }{ \ddots } } } } \\ $

asked Jun 01 '18 at 16:02

Harry Janes

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Assuming convergence, $f(x)=x+\frac{1}{f(x+1)},$ for whatever it's worth. – saulspatz Jun 01 '18 at 16:21
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@phdmba7of12 you cannot post graphics in comment section – The Integrator Jun 01 '18 at 16:35
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https://en.wikipedia.org/wiki/Gauss%27s_continued_fraction#The_series_0F1 – Will Jagy Jun 01 '18 at 17:01
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@phdmba7of12 already done here – The Integrator Jun 01 '18 at 17:19
Possible duplicate of Calculate an infinite continued fraction – Grant B. Jun 03 '18 at 22:32

Simplifying an infinite fraction

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