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The Emerson (1968, Biometrics 24, 695–701) recurrence relation has many important applications in statistics. However, the original derivation applied only to discrete distributions. In the following, a simple derivation is given that generalizes the Emerson recurrence relation to any distribution for which the necessary expectations exist. A modern application is outlined.
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Keywords: Hermite polynomials; orthonormal polynomials; spherical Legendre polynomials

Document Type: Research Article

Publication date: September 1, 2008

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