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Moment representation of Bernoulli polynomial, Euler polynomial and Gegenbauer polynomials

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  • Sun, Ping

Abstract

The Hermite polynomials can be represented to the moments of normal distribution by the work of Withers [2000. A simple expression for the multivariate Hermite polynomials. Statist. Probab. Lett. 47, 165-169]. This paper generally shows certain combinatorial polynomials and orthogonal polynomials are also the moments of random variables, such as Bernoulli polynomials, Euler polynomials, Gegenbauer polynomials.

Suggested Citation

  • Sun, Ping, 2007. "Moment representation of Bernoulli polynomial, Euler polynomial and Gegenbauer polynomials," Statistics & Probability Letters, Elsevier, vol. 77(7), pages 748-751, April.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:7:p:748-751
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    References listed on IDEAS

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    1. Willink, R., 2005. "Normal moments and Hermite polynomials," Statistics & Probability Letters, Elsevier, vol. 73(3), pages 271-275, July.
    2. Withers, C.S. & McGavin, P.N., 2006. "Expressions for the normal distribution and repeated normal integrals," Statistics & Probability Letters, Elsevier, vol. 76(5), pages 479-487, March.
    3. Withers, C. S., 2000. "A simple expression for the multivariate Hermite polynomials," Statistics & Probability Letters, Elsevier, vol. 47(2), pages 165-169, April.
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