Scientific Research Publishing

Generating Functions for Products of Special Laguerre 2D and Hermite 2D Polynomials ()

The bilinear generating function for products of two Laguerre 2D polynomials with different arguments is calculated. It corresponds to the formula of Mehler for the generating function of products of ...
scienceopen.com

A New Generating Function for Hermite Polynomials

This paper presents a new generating function for Hermite polynomials of one variable in theform of\(g(x,t)=\sum_{n=0}^{\infty }t^{n}H^{e}_{n}(x)\)and reveals its connection with incomplete gamma ...
Scientific Research Publishing

Shahwan, M.J.S. (2012) Incomplete 2D Hermite Polynomials and Their Generating Relations. Applied Mathematics & Information Sciences, 6, 109-112.

ABSTRACT: The bilinear generating function for products of two Laguerre 2D polynomials with different arguments is calculated. It corresponds to the formula of Mehler for the generating function of ...
Nature

Polyanalytic Function Theory and Hermite Polynomials

Polyanalytic function theory extends the classical theory of holomorphic functions by encompassing functions that satisfy higher‐order generalisations of the Cauchy–Riemann equations. This broader ...
IEEE

Generating Accurate Pseudo-Labels in Semi-Supervised Learning and Avoiding Overconfident Predictions via Hermite Polynomial Activations

Abstract: Rectified Linear Units (ReLUs) are among the most widely used activation function in a broad variety of tasks in vision. Recent theoretical results suggest that despite their excellent ...
JSTOR Daily

Construction of a New Class of Generating Functions of Binary Products of Some Special Numbers and Polynomials

In this paper, we derive some new symmetric properties of 𝑘-Fibonacci numbers by making use of symmetrizing operator. We also give some new generating functions for the products of some special ...