Kravchuk orthogonal polynomials

A survey of the principal works of Academician M. P. Kravchuk and his students in the area of orthogonal polynomials of a discrete variable is presented. The value of these studies for the further development of the theory, for drawing generalization, and for the construction of different applications of this class of special functions is noted.

[1]  D. Stanton.  Some q-Krawtchouk Polynomials on Chevalley Groups , 1980 .

[2]  M. V. Tratnik,et al.  Multivariable Meixner, Krawtchouk, and Meixner–Pollaczek polynomials , 1989 .

[3]  S. Karlin,et al.  The differential equations of birth-and-death processes, and the Stieltjes moment problem , 1957 .

[4]  V. B. Uvarov,et al.  Classical Orthogonal Polynomials of a Discrete Variable , 1991 .

[5]  Burton Wendroff.  On orthogonal polynomials , 1961 .

[6]  M. Hoare,et al.  Stochastic processes and special functions: On the probabilistic origin of some positive kernels associated with classical orthogonal polynomials , 1977 .

[7]  Chopped Orthogonal Polynomial Expansions—Some Discrete Cases , 1983 .

[8]  J. Meixner.  Erzeugende Funktionen der Charlierschen Polynome , 1939 .

[9]  Classical orthogonal polynomials of A discrete variable and representations of the three-dimensional rotation group , 1985 .

[10]  Morris J. Gottlieb.  Concerning Some Polynomials Orthogonal on a Finite or Enumerable Set of Points , 1938 .

[11]  D. Kershaw.  A note on orthogonal polynomials , 1970, Proceedings of the Edinburgh Mathematical Society.

[12]  P. Lesky.  Wahrscheinlichkeitsfunktionen diskreter Verteilungen als Lösungen der Pearsonschen Differenzengleichung für die diskreten klassischen Orthogonalpolynome , 1984 .

[13]  T. Koornwinder,et al.  Krawtchouk polynomials, a unification of two different group theoretic interpretations : (preprint) , 1982 .

[14]  A Property of Orthogonal Polynomial Families with Polynomial Duals , 1984 .

[15]  Mizan Rahman,et al.  Cumulative Bernoulli trials and Krawtchouk processes , 1984 .

[16]  S. Karlin,et al.  LINEAR GROWTH, BIRTH AND DEATH PROCESSES , 1958 .

[17]  P. Lesky.  Orthogonale Polynomsysteme als Lösungen Sturm-Liouvillescher Differenzengleichungen , 1962 .

[18]  W. Hahn.  Über Orthogonalpolynome, die q-Differenzengleichungen genügen , 1949 .

[19]  J. Meixner,et al.  Orthogonale Polynomsysteme Mit Einer Besonderen Gestalt Der Erzeugenden Funktion , 1934 .