[seqfan] Re: simplify the constant A186706

[israel at math.ubc.ca]

Maple 16 confirms that sum is 2*Pi/sqrt(3): 

> sum(3^m/m/binomial(2*m,m),m=1..infinity);

2/3*Pi*3^(1/2)

Or were you asking for confirmation that the integral is equal to the sum?
I don't think Maple has the Dedekind Eta function.

Robert Israel
University of British Columbia


On Jul 24 2012, Richard Mathar wrote:

>
>Can someone confirm that A186706 = 3.627598728468435
>is 2*Pi/sqrt(3) ?
>Appears as sum_{m>=1} 3^m/m/binomial(2m,m) in Lehmer's Article
>in Am. Math. Monthly 92 (1985) 449-457.
>
>RJM
>
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