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Keywords:

  • Hermite polynomials;
  • orthonormal polynomials;
  • spherical Legendre polynomials

Summary

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.