Project without external funding

Die Rolle von q-Differenzengleichungen bei der Untersuchung orthogonaler Polynome und spezieller Zahlfolgen

Project Details

Project duration: 11/2004–12/2010

Abstract

The q-calculus is a very important part of modern mathematics with applications in several mathematical disciplines: orthogonal polynomials, difference equations, transforms (Laplace, Fourier), group theory, noncommutative geometry, etc. Also, it has applications in numerous applications, such as physics, general relativity, molecular and nuclear spectroscopy, elementary particle physics and chemical physics, theory of strings.We will discuss the properties of some classes of orthogonal polynomials (classical and q-classical), hypergeometric and basic hypergeometric functions, and study the properties of some important q-operators such as the q-derivative, q-integral, q-shift, and q-difference. Some special transforms (Laplace, Fourier) and their q-analogues are studied. Relations between different classes of q-classical orthogonal polynomials and high order q-difference equations are investigated.Some special number sequences and their q-analogues (Fibonacci, Catalan) are treated. Those numbers appear in different areas of science and real life.