Some divergent trigonometric integrals

Details Some divergent trigonometric integrals Some divergent trigonometric integrals

2001-01-02

arxiv.org/abs/math/0101011v1

Mathematics

Classical Analysis and ODEs

to appear in a slightly different version in Amer. Math. Monthly

Scientific paper

Some divergent trigonometric integrals have appeared in standard tables for
many years, listed as converging. We give a simple proof that these integrals
diverge and trace their history. The original error was made when a
(startlingly) famous mathematician incorrectly differentiated under the
integral sign with some convergent integrals that depend on a paramater.

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