scholarly journals $q$-Laguerre polynomials and big $q$-Bessel functions and their orthogonality relations

1999 ◽  
Vol 6 (1) ◽  
pp. 109-127 ◽  
Author(s):  
Nicola Ciccoli ◽  
Erik Koelink ◽  
Tom H. Koornwinder
Keyword(s):  
Bessel Functions ◽  
Laguerre Polynomials ◽  
Orthogonality Relations

MORE ON FINITE TEMPERATURE ANYON SUPERCONDUCTIVITY

1992 ◽  
Vol 06 (26) ◽  
pp. 1623-1637 ◽  
Author(s):  
Y. LEBLANC ◽  
J.C. WALLET
Keyword(s):  
High Temperature ◽  
Finite Temperature ◽  
Linear Response ◽  
Bessel Functions ◽  
Laguerre Polynomials ◽  
Linear Response Theory ◽  
Threshold Temperature ◽  
Type I ◽  
Type Ii ◽  
Non Local

In the framework of finite temperature linear response theory, we analyze to a greater extent the nature of anyonic superconductivity. Using identities among Laguerre polynomials and Bessel functions, we provide simple and useful expressions for the response function in the form of high temperature expansions. The physical penetration depth as well as the Landau-Ginzburg coherence length are calculated for all temperatures. We find that for statistics restricted by n≪450, anyon superconductors are type II local (London) superconductors at low temperature and type I non-local (Pippard) superconductors at high temperature. The threshold temperature is also obtained.

Comment on “Fourier transform of hydrogen-type atomic orbitals”

2019 ◽  
Vol 97 (12) ◽  
pp. 1349-1360 ◽  
Author(s):  
Ernst Joachim Weniger
Keyword(s):  
Fourier Transform ◽  
Bessel Functions ◽  
Fourier Transforms ◽  
Laguerre Polynomials ◽  
Bound State ◽  
Atomic Orbitals ◽  
Generalized Laguerre Polynomials ◽  
Classic Result ◽  
The Fourier Transform ◽  
Finite Sum

Podolsky and Pauling (Phys. Rev. 34, 109 (1929) doi: 10.1103/PhysRev.34.109 ) were the first ones to derive an explicit expression for the Fourier transform of a bound-state hydrogen eigenfunction. Yükçü and Yükçü (Can. J. Phys. 96, 724 (2018) doi: 10.1139/cjp-2017-0728 ), who were apparently unaware of the work of Podolsky and Pauling or of the numerous other earlier references on this Fourier transform, proceeded differently. They expressed a generalized Laguerre polynomial as a finite sum of powers, or equivalently, they expressed a bound-state hydrogen eigenfunction as a finite sum of Slater-type functions. This approach looks very simple, but it leads to comparatively complicated expressions that cannot match the simplicity of the classic result obtained by Podolsky and Pauling. It is, however, possible to reproduce not only Podolsky and Pauling’s formula for the bound-state hydrogen eigenfunction, but to obtain results of similar quality also for the Fourier transforms of other, closely related, functions, such as Sturmians, Lambda functions, or Guseinov’s functions, by expanding generalized Laguerre polynomials in terms of so-called reduced Bessel functions.

An Expansion of the Laguerre Polynomials, Lαn(z)

1962 ◽  
Vol 5 (3) ◽  
pp. 229-240 ◽  
Author(s):  
Max Wyman
Keyword(s):  
Bessel Functions ◽  
Laguerre Polynomials ◽  
Image Position

By a result due to Tricomi(1), it is known that the La guerre polynomials have an expansion in terms of the Bessel functions, Jv(z), of the form1.1where the coefficients Am are determined by1.2and1.3

A New Integral Involving the Product of Bessel Functions and Associated Laguerre Polynomials

2007 ◽  
Vol 100 (3) ◽  
pp. 263-267 ◽  
Author(s):  
R. S. Alassar ◽  
H. A. Mavromatis ◽  
S. A. Sofianos
Keyword(s):  
Bessel Functions ◽  
Laguerre Polynomials

scholarly journals On Applications of Some Special Functions in Statistics

2020 ◽  
Vol 8 (6) ◽  
pp. 1902-1908
Keyword(s):  
Characteristic Function ◽  
Laplace Transform ◽  
Bessel Functions ◽  
Special Functions ◽  
Probability Distributions ◽  
Laguerre Polynomials ◽  
Real Life ◽  
Moment Generating Function ◽  
Cumulative Density Function ◽  
Modified Bessel Functions

In this paper we will introduce some probability distributions with help of some special functions like Gamma, kGamma functions, Beta, k-Beta functions, Bessel, modified Bessel functions and Laguerre polynomials and in mathematical analysis used Laplace transform. We will also obtain their cumulative density function, expected value, variance, Moment generating function and Characteristic function. Some characteristics and real life applications will be computed in tabulated for these distributions

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