Some divergent trigonometric integrals
经典分析与常微分方程
2007-05-23 v1
摘要
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.
引用
@article{arxiv.math/0101011,
title = {Some divergent trigonometric integrals},
author = {Erik Talvila},
journal= {arXiv preprint arXiv:math/0101011},
year = {2007}
}
备注
to appear in a slightly different version in Amer. Math. Monthly