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June 22

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Generalization of a Certain Formula for Pi

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Let and Then, assuming convergence, we have Thus, for we have for instance. Now, for we have and My question would be with what constant to replace in general, for different values of A and B, so that the limit in question should converge to a finite non-zero quantity. In other words, if what is the general formula for  ? Thank you. — 79.118.171.25 (talk) 22:57, 22 June 2015 (UTC)[reply]

Apparently, and the limit in question is the square root of the Paris constant. — 79.118.171.25 (talk) 03:07, 23 June 2015 (UTC)[reply]
I get . My idea is to let and write its recurrence formula. The behavior for small is dictated by the linear term of its Maclaurin series. From there it's not hard to understand the behavior of and find . Egnau (talk) 03:40, 23 June 2015 (UTC)[reply]
I arrived just these past few minutes at the same conclusion, and wanted to post it, but was unable to connect. :-) Thanks ! — 79.113.226.120 (talk) 03:53, 23 June 2015 (UTC)[reply]
And in general, for we have where is a root of 79.113.226.120 (talk) 10:08, 23 June 2015 (UTC)[reply]
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