Sunday, January 04, 2015

[1004.2453] Wallis-Ramanujan-Schur-Feynman

[1004.2453] Wallis-Ramanujan-Schur-Feynman:



"One of the earliest examples of analytic representations for π is given by an infinite product provided by Wallis in 1655. The modern literature often presents this evaluation based on the integral formula
2π∫∞0dx(x2+1)n+1=122n(2nn).
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."



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