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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

The calculation of multidimensional Hermite polynomials and Gram-Charlier coefficients


Authors: S. Berkowitz and F. J. Garner
Journal: Math. Comp. 24 (1970), 537-545
MSC: Primary 65.25
Corrigendum: Math. Comp. 25 (1971), 947.
Corrigendum: Math. Comp. 25 (1971), 947.
MathSciNet review: 0273784
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Abstract | References | Similar Articles | Additional Information

Abstract: The paper documents derivations of: (a) a recurrence relation for calculating values of multidimensional Hermite polynomials,

(b) a recurrence relation for calculating an approximation to the Gram-Charlier coefficients of the probability density distribution associated with a random process, based on (a),

(c) an efficient algorithm to utilize the formulae in (a) and (b).


References [Enhancements On Off] (What's this?)

  • [1] Paul Appell, Analyse mathématique à l’usage des candidats au certificat de mathématiques générales et aux grandes écoles. Tome I. Analyse des courbes, surfaces et fonctions usuelles, intégrales simples, Gauthier-Villars, Paris, 1951 (French). 6th ed. MR 0038393 (12,397b)
  • [2] A. Erdélyi, et al., Higher Transcendental Functions, McGraw-Hill, New York, 1953. MR 15, 419.
  • [3] J. Kampé de Fériet, The Gram-Charlier Approximation of the Normal Law and the Statistical Description of a Homogeneous Turbulent Flow near Statistical Equilibrium, Applied Mathematics Laboratory, NSRDC Report No. 2013, March, 1966.
  • [4] S. Kh. Sirazhdinov, Contribution to the Theory of Hermite Multidimensional Polynomials, Candidate Dissertation, Tashkent State University, USSR, 1949. (Russian)
  • [5] S. Ya. Vilenkin, "Determination of the maximum time (critical path time) distribution," Avtomat. i Telemeh., v. 1965, no. 7, pp. 1247-1252 = Automat. Remote Control, v. 1965, no. 7, pp. 1333-1337.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1970-0273784-2
PII: S 0025-5718(1970)0273784-2
Keywords: Multidimensional Hermite polynomials, Gram-Charlier series, recurrence relations, Gaussian probability density, normal distributions
Article copyright: © Copyright 1970 American Mathematical Society