沃利斯-拉马努金-舒尔-费曼
Wallis-Ramanujan-Schur-Feynman
摘要：
最早的例子之一的解析表示$π$是由一个无穷乘积提供的沃利斯在1655年。现代文献经常提出这种评价的基础上的积分公式$$ \frac{2}π \int_0^\infty \frac{dx}{(x^2+1)^{n+1}} = \frac{1}{2^{2n}} \binom{2n}{n}. $$在试图了解的行为，这种积分时，被积函数被取代的逆产品的不同的二次因子，作者遇到的关系，一些公式的拉马努金，表达式涉及舒尔函数，松原和已出现的背景下，费曼图。
英文摘要：
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 $$ \frac{2}π \int_0^\infty \frac{dx}{(x^2+1)^{n+1}} = \frac{1}{2^{2n}} \binom{2n}{n}. $$ 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.
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