×

Establishment of a generating function and a Chebyshev-like differential equation for the heat equation related \(m\)-Boubaker polynomials. (English) Zbl 1180.33028

Summary: We try to find a generating function for the \(m\)-Boubaker polynomials. Since their first definition as an analytical tool that led to a solution to the heat equation, the Boubaker polynomials have been dealt with as non-orthogonal sequences that don’t obey to any known Legendre-Laguerre type characteristic differential equation. This generating function is a guide to establish a second order differential equation, which is inhomogeneous and not characteristic as long as it uses an other special function.

MSC:

33E20 Other functions defined by series and integrals
33E30 Other functions coming from differential, difference and integral equations
33E99 Other special functions
41A30 Approximation by other special function classes
41A55 Approximate quadratures
PDFBibTeX XMLCite