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 ...

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 ...

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 ...

This paper presents the connections between univariate and bivariate Hermite polynomials and associated differential equations with specific representations of sl (2, R) algebra whose Cartan ...

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 ...

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 ...

Hermite polynomials and functions are widely used for scientific and engineering problems. Although it is known that using the scaled Hermite function instead of the standard one can significantly ...