scholarly journals Multiple orthogonal polynomials associated with confluent hypergeometric functions

2020 ◽  
Vol 260 ◽  
pp. 105484
Author(s):  
Hélder Lima ◽  
Ana Loureiro
Keyword(s):  
Orthogonal Polynomials ◽  
Hypergeometric Functions ◽  
Confluent Hypergeometric Functions ◽  
Multiple Orthogonal Polynomials

scholarly journals Neoteric formulas of the monic orthogonal Chebyshev polynomials of the sixth-kind involving moments and linearization formulas

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Waleed M. Abd-Elhameed ◽  
Youssri H. Youssri
Keyword(s):  
Orthogonal Polynomials ◽  
Chebyshev Polynomials ◽  
Hypergeometric Functions ◽  
Connection Coefficients ◽  
Current Article ◽  
In Virtue Of ◽  
Connection Formulas

AbstractThe principal aim of the current article is to establish new formulas of Chebyshev polynomials of the sixth-kind. Two different approaches are followed to derive new connection formulas between these polynomials and some other orthogonal polynomials. The connection coefficients are expressed in terms of terminating hypergeometric functions of certain arguments; however, they can be reduced in some cases. New moment formulas of the sixth-kind Chebyshev polynomials are also established, and in virtue of such formulas, linearization formulas of these polynomials are developed.

scholarly journals On the birthday problem: some generalizations and applications

2003 ◽  
Vol 2003 (60) ◽  
pp. 3827-3840 ◽  
Author(s):  
P. N. Rathie ◽  
P. Zörnig
Keyword(s):  
Probability Distribution ◽  
Random Graph ◽  
Generating Functions ◽  
Hypergeometric Functions ◽  
Exact Probability ◽  
Confluent Hypergeometric Functions ◽  
Birthday Problem ◽  
Exact Probability Distribution

We study the birthday problem and some possible extensions. We discuss the unimodality of the corresponding exact probability distribution and express the moments and generating functions by means of confluent hypergeometric functionsU(−;−;−)which are computable using the software Mathematica. The distribution is generalized in two possible directions, one of them consists in considering a random graph with a single attracting center. Possible applications are also indicated.

scholarly journals Strong asymptotics for the Pollaczek multiple orthogonal polynomials

2015 ◽  
Vol 92 (3) ◽  
pp. 709-713
Author(s):  
A. I. Aptekarev ◽  
G. López Lagomasino ◽  
A. Martínez-Finkelshtein
Keyword(s):  
Orthogonal Polynomials ◽  
Strong Asymptotics ◽  
Multiple Orthogonal Polynomials

Multiple Orthogonal Polynomials on the Unit Circle

2007 ◽  
Vol 28 (2) ◽  
pp. 173-197 ◽  
Author(s):  
Judit Minguez Ceniceros ◽  
Walter Van Assche
Keyword(s):  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Multiple Orthogonal Polynomials

scholarly journals FOUR-PARTICLE ANYON EXCITON: BOSON APPROXIMATION

1995 ◽  
Vol 09 (02) ◽  
pp. 123-133 ◽  
Author(s):  
M. E. Portnoi ◽  
E. I. Rashba
Keyword(s):  
Angular Momentum ◽  
Electron Density ◽  
Ground State ◽  
Hypergeometric Functions ◽  
Energy Levels ◽  
Confluent Hypergeometric Functions ◽  
Full Symmetry ◽  
Hole Confinement ◽  
Boson Approximation

A theory of anyon excitons consisting of a valence hole and three quasielectrons with electric charges –e/3 is presented. A full symmetry classification of the k = 0 states is given, where k is the exciton momentum. The energy levels of these states are expressed by quadratures of confluent hypergeometric functions. It is shown that the angular momentum L of the exciton ground state depends on the distance between the electron and hole confinement planes and takes the values L = 3n, where n is an integer. With increasing k the electron density shows a spectacular splitting on bundles. At first a single anyon splits off of the two-anyon core, and finally all anyons become separated.

scholarly journals IX.—The Confluent Hypergeometric Functions of Two Variables

1922 ◽  
Vol 41 ◽  
pp. 73-96 ◽  
Author(s):  
Pierre Humbert
Keyword(s):  
Hypergeometric Functions ◽  
Confluent Hypergeometric Functions ◽  
Functions Of Two Variables

This memoir is devoted to the study of certain new functions, which may be regarded as limiting cases of the “hypergeometric functions of two variables” discovered by Appell.

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