Irrationality proofs a la Hermite

摘要

In [1] Niven used the integral H_n = ∫_0~π (x~n(π-x)~n)! sin x dx to give a well-known proof of the irrationality of π. Recently Zhou andMarkov [2] used a recurrence relation satisfied by this integral to present analternative proof which may he more direct than Niven's.