# 2014-14 Integration and integrality

Prove or disprove that for all positive integers $$m$$ and $$n$$, $f(m,n)=\frac{2^{3(m+n)-\frac12} }{{\pi}} \int_0^{\pi/2} \sin^{ 2n – \frac12 }\theta \cdot \cos^{2m+\frac12}\theta \, d\theta$  is an integer.

(A typo is fixed on Saturday.)

GD Star Rating