Jackson integral

English

Etymology

Introduced by Frank Hilton Jackson.

Noun

Jackson integral (plural Jackson integrals)

1. (mathematics) The series expansion $\int _{0}^{a}f(x)\,{\rm {d}}_{q}x=(1-q)\,a\sum _{k=0}^{\infty }q^{k}f(q^{k}a).$ for real variable a and function of a real variable f(x).
   • 1993, D. B. Fuks, Unconventional Lie Algebras, page 52:

     The Jackson integral enjoys several elementary properties of the usual integral.

   • 2001, Publications of the Research Institute for Mathematical Sciences, page 72:

     By taking residues, we can represent this integral in terms of a Jackson integral.

   • 2012, Simon Gindikin, James Lepowsky, Robert Wilson, Functional Analysis on the Eve of the 21st Century, page 11:

     We can find elliptic solutions to Yang-Baxter equations as connection functions among Jackson integrals giving asymptotics corresponding to asymptotic regions […]