Hahn Difference Operator and Associated JacksonNrlund Integrals
This paper is devoted for a rigorous investigation of Hahns difference operator and the associated calculus. Hahns difference operator generalizes both the difference operator and Jacksons q-difference operator. Unlike these two operators, the calculus associated with Hahns difference operator receives no attention. In particular, its right inverse has not been constructed before. We aim to establish a calculus of differences based on Hahns difference operator. We construct a right inverse of Hahns operator and study some of its properties. This inverse also generalizes both Nrlund sums and the Jackson q-integrals. We also define families of corresponding exponential and trigonometric functions which satisfy first and second order difference equations, respectively.
hahns operator nrlund sums difference equations q-difference equations jackson q-integral