Remote Access Mathematics of Computation
Green Open Access

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
DOI: https://doi.org/10.1090/S0025-5718-1970-0273784-2
Corrigendum: Math. Comp. 25 (1971), 947.
Corrigendum: Math. Comp. 25 (1971), 947.
MathSciNet review: 0273784
Full-text PDF Free Access

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?)

  • 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
  • A. Erdélyi, et al., Higher Transcendental Functions, McGraw-Hill, New York, 1953. MR 15, 419. 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. S. Kh. Sirazhdinov, Contribution to the Theory of Hermite Multidimensional Polynomials, Candidate Dissertation, Tashkent State University, USSR, 1949. (Russian) 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.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65.25

Retrieve articles in all journals with MSC: 65.25


Additional Information

Keywords: Multidimensional Hermite polynomials, Gram-Charlier series, recurrence relations, Gaussian probability density, normal distributions
Article copyright: © Copyright 1970 American Mathematical Society