scholarly journals On partly bilateral and partly unilateral generating functions

1986 ◽  
Vol 28 (2) ◽  
pp. 240-245 ◽  
Author(s):  
M. A. Pathan ◽  
Yasmeen
Keyword(s):  
Generating Functions ◽  
Laguerre Polynomials ◽  
Partial Derivatives ◽  
Starting Point ◽  
Generating Relations

AbstractThe purpose of this work is to begin the development of a theory of generating functions that will not only include the generating functions which are partly bilateral and partly unilateral but also provide a set of expansions, by taking successive partial derivatives with respect to one of the variables of the generating relations. Our starting point is a result of Exton [4] on associated Laguerre polynomials whose application gives certain generating functions of the polynomials of Jacobi and Appell, and functions of n variables of Lauricella.

scholarly journals On generalized Lagrange–Hermite–Bernoulli and related polynomials

2020 ◽  
Vol 23 (2) ◽  
pp. 211-224
Author(s):  
Waseem A. Khan ◽  
M. A. Pathan
Keyword(s):  
Generating Functions ◽  
Special Functions ◽  
Laguerre Polynomials ◽  
Point Of View ◽  
Generalized Polynomials ◽  
New Class ◽  
The Past ◽  
The Family ◽  
Generating Relations ◽  
High Degree

We introduce a new class of generalized polynomials, ascribed to the family of Hermite, Lagrange, Bernoulli, Miller–Lee, and Laguerre polynomials and of their associated forms. These polynomials can be expressed in the form of generating functions, which allow a high degree of exibility for the formulation of the relevant theory. We develop a point of view based on generating relations, exploited in the past, to study some aspects of the theory of special functions. We propose a fairly general analysis allowing a transparent link between different forms of special polynomials.

scholarly journals On the p,q-Humbert Functions from the View Point of the Generating Function Method

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Ayman Shehata
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Function Method ◽  
Recurrence Relations ◽  
View Point ◽  
Starting Point ◽  
Explicit Representations

The main object of the present paper is to construct new p,q-analogy definitions of various families of p,q-Humbert functions using the generating function method as a starting point. This study shows a class of several results of p,q-Humbert functions with the help of the generating functions such as explicit representations and recurrence relations, especially differential recurrence relations, and prove some of their significant properties of these functions.

scholarly journals The Electrical Conductivity of a Partially Ionized Argon-Potassium Plasma in a Magnetic Field

1966 ◽  
Vol 21 (9) ◽  
pp. 1468-1470 ◽  
Author(s):  
W. Feneberg
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Laguerre Polynomials ◽  
Lorentz Gas ◽  
Small Deviations ◽  
Starting Point ◽  
Potassium Plasma ◽  
Partially Ionized ◽  
Ramsauer Effect ◽  
The Magnetic Field

In the case of small deviations from thermal equilibrium the second ENSKOG approximation is used as a starting point for solving the BOLTZMANN equation of the electrons in a partially ionized plasma. The distribution function is expanded according to LAGUERRE polynomials up to the order of 3. In this order the electrical conductivity of a LORENTZ gas, which is known exactly, is obtained to an accuracy of roughly 5%. The approximation tested in this way was then used to calculate the conductivity of an argon-potassium mixture at electron temperatures between 2000°K and 3500°K.If only he collisions between electrons and argon atoms were to be considered, the electrical conductivity in the absence of a magnetic field would, in view of the RAMSAUER effect, be greater by a factor of 2.8 than that obtained with an infinitely strong magnetic field. When the interaction with the potassium atoms and the COULOMB interaction are taken into account as well the conductivity in the magnetic field varies by about 20%.

scholarly journals Some generating functions of Laguerre polynomials

1987 ◽  
Vol 10 (3) ◽  
pp. 531-534 ◽  
Author(s):  
Bidyut Kumar Guha Thakurta
Keyword(s):  
Generating Functions ◽  
Laguerre Polynomials

In this note a class of interesting generating relation, which is stated in the form of theorem, involving Laguerre polynomials is derived. Some applications of the theorem are also given here.

Classical Orthogonal Polynomials as Moments

1997 ◽  
Vol 49 (3) ◽  
pp. 520-542 ◽  
Author(s):  
Mourad E. H. Ismail ◽  
Dennis Stanton
Keyword(s):  
Orthogonal Polynomials ◽  
Generating Functions ◽  
Laguerre Polynomials ◽  
Classical Orthogonal Polynomials ◽  
Ultraspherical Polynomials

AbstractWe show that the Meixner, Pollaczek, Meixner-Pollaczek, the continuous q-ultraspherical polynomials and Al-Salam-Chihara polynomials, in certain normalization, are moments of probability measures.We use this fact to derive bilinear and multilinear generating functions for some of these polynomials. We also comment on the corresponding formulas for the Charlier, Hermite and Laguerre polynomials.

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