On Orthogonal Appell-Like Polynomials in Non-Gaussian Analysis

• Date: 2001
• Main Authors: Kalyuzhnyi, A. A., Kachanovskii, N. A., Калюжный, А. А., Качановский, Н. А.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2001
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4311
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We study an example of the construction of a non-Gaussian analysis using orthogonal generalized Appell-like polynomials with the generating function $$\frac{1}{{\sqrt {1 - 2a{\lambda + \lambda }^{2}} } }\cos \left( {\sqrt x \frac{1}{2}\int\limits_{0}^{\lambda } {\frac{{du}}{{\sqrt {u - 2au^2 + u^3...