Talk:Bernoulli polynomials

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[edit] Error in integrals?

Definite integrals
\int_0^1 B_n(t) B_m(t)\,dt = (-1)^{n-1} \frac{m! n!}{(m+n)!} B_{n+m} \quad \mbox { for } m,n \ge 1
\int_0^1 E_n(t) E_m(t)\,dt = (-1)^{n} 4 (2^{m+n+2}-1)\frac{m! n!}{(m+n+2)!} B_{n+m+2}

Should it be (−1)n + m instead of (−1)n − 1? Obviously the integrals must depend in a symmetrical way on the two variables n and m. Michael Hardy 19:18, 7 September 2006 (UTC)

Nope, but either m or n will do. If one is odd and the other even, the right-hand side is zero. So the sign only matters when they are both odd or both even, and in that case it is sufficient to look at one of them. Fredrik Johansson 19:51, 7 September 2006 (UTC)

Very nice. Maybe that should be added to the article. Michael Hardy 20:23, 7 September 2006 (UTC)