Taiwanese Journal of Mathematics

An Expectation Formula Based on a Maclaurin Expansion

Mingjin Wang

Full-text: Open access

Abstract

In this paper, we obtain an expectation formula with respect to the $q$-probability distribution $W(x,y;q)$ based on a Maclaurin expansion. The formula has many applications in mathematics. Some of the applications are also given, which include a probability version of the Al-Salam and Verma $q$-integral.

Article information

Source
Taiwanese J. Math., Volume 23, Number 3 (2019), 563-574.

Dates
Received: 3 April 2018
Revised: 29 July 2018
Accepted: 1 August 2018
First available in Project Euclid: 10 August 2018

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1533866420

Digital Object Identifier
doi:10.11650/tjm/180802

Mathematical Reviews number (MathSciNet)
MR3952240

Zentralblatt MATH identifier
07068563

Subjects
Primary: 60E05: Distributions: general theory 05A30: $q$-calculus and related topics [See also 33Dxx] 33D15: Basic hypergeometric functions in one variable, $_r\phi_s$

Keywords
the probability distribution $W(x,y;q)$ the Maclaurin expansion $q$-integral the Lebesgue's dominated convergence theorem the Bernoulli numbers

Citation

Wang, Mingjin. An Expectation Formula Based on a Maclaurin Expansion. Taiwanese J. Math. 23 (2019), no. 3, 563--574. doi:10.11650/tjm/180802. https://projecteuclid.org/euclid.twjm/1533866420


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References

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