English

Necessary and sufficient conditions for differentiating under the integral sign

Classical Analysis and ODEs 2007-05-23 v1

Abstract

We give necessary and sufficient conditions for differentiating under the integral sign an integral that depends on a parameter. The conditions require the equality of two iterated integrals and depend on being able to integrate every derivative. The Henstock integral is thus used in an essential way.

Keywords

Cite

@article{arxiv.math/0101012,
  title  = {Necessary and sufficient conditions for differentiating under the integral sign},
  author = {Erik Talvila},
  journal= {arXiv preprint arXiv:math/0101012},
  year   = {2007}
}
R2 v1 2026-07-22T16:36:38.058Z