Jackson integral

noun

The series expansion ∫₀ᵃf(x),rm d_qx=(1-q),a∑ₖ₌₀ ᪲qᵏf(qᵏa). for real variable a and function of a real variable f(x).

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Meanings

nounJackson integral (plural Jackson integrals)

plural Jackson integrals

  1. mathematicsThe series expansion ∫₀ᵃf(x),rm d_qx=(1-q),a∑ₖ₌₀ ᪲qᵏf(qᵏa). for real variable a and function of a real variable f(x).

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

    1993, D. B. Fuks, Unconventional Lie Algebras, page 52
    2 more examples

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

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

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

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

Origin

Introduced by Frank Hilton Jackson.

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Cite this entry
APA

Jackson integral. (n.d.). In WatkinsX Dictionary. Retrieved November 3, 2026, from https://dictionary.watkinsx.com/word/Jackson%20integral

MLA

“Jackson integral.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Jackson%20integral. Accessed November 3, 2026.

Chicago

WatkinsX Dictionary, s.v. “Jackson integral,” accessed November 3, 2026, https://dictionary.watkinsx.com/word/Jackson%20integral.

Source: Jackson integral on Wiktionary, CC BY-SA 4.0.