Wallis-Ramanujan-Schur-Feynman

Details Wallis-Ramanujan-Schur-Feynman Wallis-Ramanujan-Schur-Feynman

2010-04-14

arxiv.org/abs/1004.2453v1

Mathematics

Classical Analysis and ODEs

18 pages, 1 figure

Scientific paper

One of the earliest examples of analytic representations for $\pi$ is given by an infinite product provided by Wallis in 1655. The modern literature often presents this evaluation based on the integral formula $$ \frac{2}{\pi} \int_0^\infty \frac{dx}{(x^2+1)^{n+1}} = \frac{1}{2^{2n}} \binom{2n}{n}. $$ In trying to understand the behavior of this integral when the integrand is replaced by the inverse of a product of distinct quadratic factors, the authors encounter relations to some formulas of Ramanujan, expressions involving Schur functions, and Matsubara sums that have appeared in the context of Feynman diagrams.

Affiliated with

Also associated with

No associations

Rating

Wallis-Ramanujan-Schur-Feynman does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Wallis-Ramanujan-Schur-Feynman, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Wallis-Ramanujan-Schur-Feynman will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-528245