shaum spiegel errata
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A brief note dated 10.23.09 and initialed PhL, pointing out a bug in Schaum's outline problem 15.28. Phil works the integral with Maple for integer m and n, showing the result is zero when m+n is even and 2m/(m^2-n^2) when m+n is odd, so the book has odd and even swapped. He notes a web integral list appears to copy the error and that a CRC math handbook gives the correct form.
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Bug in Schaum p 96 15.28 PhL 10.23.09
The problem: suppose m = n. Then m+n = even, and integral equals 2m/0 = ∞.
Resolution: According to Maple,
If m and n are both integers, we can write this as
(m(-1)m+n + 0 - m ) / (n2-m2) = m [(-1)m+n - 1] / (n2-m2)
= m[1 - (-1)m+n] / (m2- n2)
If m+n = even, numerator is 0. If m+n = odd, result is 2m/(m2-n2).
Amazingly Schaum has the words "odd" and "even" swapped! A web SOS website I think has just stolen its integral list from Schaum
and they propagate the error. I finally found a correct statement of my integral in a CRC math book I downloaded from the Russian site, to wit,