Continued fraction for $[1,2,3,4,5,6,\dots]$

Asked Apr 14 '15 at 17:02

Active Apr 14 '15 at 17:02

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Any continued fraction that does not terminate or repeat can't be rational or a quadratic irrational. It is not hard to write something that does not fit these two categories.

Can we still get a closed form for something like: $$ [1,2,3,4,5, \dots ] = 1 + \cfrac{1}{2+\cfrac{1}{3+\cfrac{1}{\dots}}}$$

asked Apr 14 '15 at 17:02

cactus314

24,438

1

http://mathworld.wolfram.com/ContinuedFractionConstant.html – Jack D'Aurizio Apr 14 '15 at 17:05
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Such a constant can be written as the ratio of two modified Bessel functions of the first kind evaluated at $2$. – Jack D'Aurizio Apr 14 '15 at 17:06

Continued fraction for $[1,2,3,4,5,6,\dots]$

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