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Teor. Veroyatnost. i Primenen., 2001, Volume 46, Issue 3, Pages 585–592 (Mi tvp3907)  

This article is cited in 7 scientific papers (total in 7 papers)

Short Communications

Polynomials Orthogonal with Respect to the Multinomial Distribution and the Factorial-Power Formalism

V. I. Khokhlov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: A new combinatorial formalism is developed and applied to obtain new forms for Krawtchouk and Poisson–Charlier polynomials. These forms are used to obtain linear representations for pairwise products of such polynomials. As another application a family of polynomials orthogonal with respect to the multinomial distribution is established.

Keywords: binomial distribution, Poisson distribution, multinomial distribution, Krawtchouk polynomials, Poisson–Charlier polynomials, factorial-power polynomials, polynomials orthogonal with respect to multinomial distribution, combinatorial identities, Lerch identity.

DOI: https://doi.org/10.4213/tvp3907

Full text: PDF file (804 kB)

English version:
Theory of Probability and its Applications, 2002, 46:3, 529–536

Bibliographic databases:

Received: 01.08.2001

Citation: V. I. Khokhlov, “Polynomials Orthogonal with Respect to the Multinomial Distribution and the Factorial-Power Formalism”, Teor. Veroyatnost. i Primenen., 46:3 (2001), 585–592; Theory Probab. Appl., 46:3 (2002), 529–536

Citation in format AMSBIB
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\transl
\jour Theory Probab. Appl.
\yr 2002
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\pages 529--536
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. V. Prokhorov, O. V. Viskov, V. I. Khokhlov, “Analogues of the Chernoff inequality for negative binomial ditribution”, Theory Probab. Appl., 50:2 (2006), 327–330  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Harremoes P., Johnson O., Kontoyiannis I., “Thinning and Information Projections”, IEEE International Symposium on Information Theory Proceedings, 2008, 2644–2648  crossref  mathscinet  isi  scopus
    3. Withers Ch.S., Nadarajah S., “Orthogonal Polynomials Via Random Variables”, Util Math, 86 (2011), 95–114  mathscinet  zmath  isi  elib
    4. Area I., Godoy E., “On Limit Relations Between Some Families of Bivariate Hypergeometric Orthogonal Polynomials”, J. Phys. A-Math. Theor., 46:3 (2013), 035202  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    5. G. I. Ivchenko, Yu. I. Medvedev, V. A. Mironova, “Analiz spektra sluchainykh simmetricheskikh bulevykh funktsii”, Matem. vopr. kriptogr., 4:1 (2013), 59–76  mathnet  crossref
    6. G. I. Ivchenko, Yu. I. Medvedev, V. A. Mironova, “Mnogochleny Kravchuka i ikh primeneniya v zadachakh kriptografii i teorii kodirovaniya”, Matem. vopr. kriptogr., 6:1 (2015), 33–56  mathnet  crossref  mathscinet  elib
    7. O. V. Viskov, V. I. Khokhlov, “Four areas of Yu. V. Prokhorov's studies and their perspectives”, Theory Probab. Appl., 60:2 (2016), 336–342  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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