|
вот Вам целая книга
Dunkl, Charles F.; Xu, Yuan Orthogonal polynomials of several variables. Encyclopedia of Mathematics and its Applications, 81. Cambridge University Press, Cambridge, 2001. xvi+390 pp.
По аппроксимации распределений,
см
Severini, Thomas A. Elements of distribution theory. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge, 2005. xii+515 pp. ISBN: 978-0-521-84472-7; 0-521-84472-X
Barndorff-Nielsen, O. E.; Cox, D. R. Asymptotic techniques for use in statistics. Monographs on Statistics and Applied Probability. Chapman & Hall, London, 1989. x+252 pp. ISBN: 0-412-31400-2
Farrell, Roger H. Multivariate calculation. Use of the continuous groups. Springer Series in Statistics. Springer-Verlag, New York, 1985. xvi+376 pp. ISBN: 0-387-96049-X
и статьи
Beerends, R. J. Chebyshev polynomials in several variables and the radial part of the Laplace-Beltrami operator. Trans. Amer. Math. Soc. 328 (1991), no. 2, 779--814.
Fernández, Lidia; Pérez, Teresa E.; Piñar, Miguel A. On multivariate classical orthogonal polynomials. Rend. Circ. Mat. Palermo (2) Suppl. No. 76 (2005), 315--329.
Bultheel, A.; Cuyt, A.; Van Assche, W.; Van Barel, M.; Verdonk, B. Generalizations of orthogonal polynomials. J. Comput. Appl. Math. 179 (2005), no. 1-2, 57--95.
Goldstein, Larry; Reinert, Gesine Distributional transformations, orthogonal polynomials, and Stein characterizations. J. Theoret. Probab. 18 (2005), no. 1, 237--260.
Kim, Y. J.; Kwon, K. H.; Lee, J. K. Multi-variate orthogonal polynomials and second order partial differential equations. Commun. Appl. Anal. 6 (2002), no. 4, 479--504.
Benabidallah, A.; Cherruault, Y.; Tourbier, Y. Approximation of several variables functions by products or sums of one variable functions. Kybernetes 31 (2002) no. 5, 701--714.
Benouahmane, Brahim; Cuyt, Annie Properties of multivariate homogeneous orthogonal polynomials. J. Approx. Theory 113 (2001), no. 1, 1--20.
Gupta, A. K. Orthogonal polynomials and truncated multivariate distributions. Proceedings of the Sixth Conference on Probability Theory (Bra\c sov, 1979), pp. 77--90, Ed. Acad. R.S. România, Bucharest, 1981.
Elandt-Johnson, Regina C. Multi-dimensional orthogonal polynomials for certain models in multivariate analysis. Sankhya Ser. B 28 1966 191--198.
|
