scholarly journals On Some Families of Complex Hermite Polynomials and their Applications to Physics

2015 ◽  
pp. 157-171
Author(s):  
F. Balogh ◽  
Nurisya M. Shah ◽  
S. Twareque Ali
Keyword(s):  
Hermite Polynomials ◽  
Complex Hermite Polynomials

scholarly journals On the complex Hermite polynomials

Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 409-420
Author(s):  
Zhi-Guo Liu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Generating Function ◽  
Poisson Kernel ◽  
Hermite Polynomials ◽  
Addition Formula ◽  
Partial Differential ◽  
Expansion Theorem ◽  
New Approach ◽  
Complex Hermite Polynomials

In this paper we use a set of partial differential equations to prove an expansion theorem for multiple complex Hermite polynomials. This expansion theorem allows us to develop a systematic and completely new approach to the complex Hermite polynomials. Using this expansion, we derive the Poisson Kernel, the Nielsen type formula, the addition formula for the complex Hermite polynomials with ease. A multilinear generating function for the complex Hermite polynomials is proved.

scholarly journals D-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization

2015 ◽  
Author(s):  
S. Twareque Ali ◽  
◽  
Fabio Bagarello ◽  
Jean Pierre Gazeau ◽  
◽  
...  
Keyword(s):  
Hermite Polynomials ◽  
Complex Hermite Polynomials

The application of Hermite polynomials to risk allocation

2016 ◽  
Vol 18 (3) ◽  
pp. 77-110
Author(s):  
Francois Buet-Golfouse ◽  
Anthony Owen
Keyword(s):  
Hermite Polynomials ◽  
Risk Allocation

scholarly journals Some Properties Involving q-Hermite Polynomials Arising from Differential Equations and Location of Their Zeros

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1168
Author(s):  
Cheon Seoung Ryoo ◽  
Jung Yoog Kang
Keyword(s):  
Differential Equations ◽  
Hermite Polynomials ◽  
Real Numbers ◽  
Different Types

Hermite polynomials are one of the Apell polynomials and various results were found by the researchers. Using Hermit polynomials combined with q-numbers, we derive different types of differential equations and study these equations. From these equations, we investigate some identities and properties of q-Hermite polynomials. We also find the position of the roots of these polynomials under certain conditions and their stacked structures. Furthermore, we locate the roots of various forms of q-Hermite polynomials according to the conditions of q-numbers, and look for values which have approximate roots that are real numbers.

scholarly journals A New Class of Higher-Order Hypergeometric Bernoulli Polynomials Associated with Lagrange–Hermite Polynomials

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 648
Author(s):  
Ghulam Muhiuddin ◽  
Waseem Ahmad Khan ◽  
Ugur Duran ◽  
Deena Al-Kadi
Keyword(s):  
Generating Function ◽  
Functional Equations ◽  
Laguerre Polynomials ◽  
Hermite Polynomials ◽  
Bernoulli Polynomials ◽  
Higher Order ◽  
New Class

The purpose of this paper is to construct a unified generating function involving the families of the higher-order hypergeometric Bernoulli polynomials and Lagrange–Hermite polynomials. Using the generating function and their functional equations, we investigate some properties of these polynomials. Moreover, we derive several connected formulas and relations including the Miller–Lee polynomials, the Laguerre polynomials, and the Lagrange Hermite–Miller–Lee polynomials.

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