The Method of Differentiating Under The Integral Sign

By Gert Almkvist and Doron Zeilberger.

Appeared in J. Symbolic Computation 10(1990), 571-591.

Ken Wilson once said that yesterday's tricks are today's method. This article makes a theory out of Richard Feynman's favorite trick for doing (ordinary, not path) integrals.

(Plain ) .tex version (23 pages)

.dvi version (for previewing)

.ps version

.pdf version

Note added with the TeX version (Dec. 15, 1999): The Almkvist-Zeilberger algorithm is implemented in the package EKAHD, but instead of calling the procedure duis, like we did in the earlier version referred to in the paper, we call it AZd and AZc, for the discrete and continuous versions, respectively.
Note: The present Plain TeX version was obtained by applying my TroffToTeX translator to the original Troff source file

Doron Zeilberger's List of Papers

Doron Zeilberger's Home Page