A GENERALIZED EMERSON RECURRENCE RELATION |
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| Authors: | J C W Rayner O Thas B De Boeck |
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| Institution: | 1. School of Mathematical and Physical Sciences, University of Newcastle, University Drive, Callaghan NSW 2308, Australia. e‐mail:;2. Department of Applied Mathematics, Biometrics and Process Control, Ghent University, B‐9000 Gent, Belgium. |
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| Abstract: | 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 |
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