And Another

Calculus Level 4

x = 1 + 1 2 + 1 3 + 1 4 + 1 5 + … \large x=1+\frac{1}{2+\frac{1}{3+\frac{1}{4+\frac{1}{5+\dots}}}}

Find x x to 3 decimal places. (Sequel to this problem .)

Bonus : Can x x be written in terms of a constant? If so, how?


The answer is 1.433.

Blan Morrison by Blan Morrison , 18, USA

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1 solution

Aaghaz Mahajan
Nov 18, 2018

The answer is terms of Bessel Functions................Follow the link in the previous problem............. @Blan Morrison I think that is where you are getting these problems??? :)

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@Otto Bretscher Sir, do you have any proof for the closed form of this constant??

Aaghaz Mahajan - 2 years, 6 months ago

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This continued fraction can be derived from a method from gauss and the hypergeometric function 0 F 1 _0F_1 .

Julian Poon - 2 years, 6 months ago

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Ohhh I see...........Thanks!! :)

Aaghaz Mahajan - 2 years, 6 months ago

Thanks for answering while I was sleeping, Julian ;)

Otto Bretscher - 2 years, 6 months ago

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