On the relation between global properties of linear difference and differential equations with polynomial coefficients. II
[For part I see ibid. 113, No. 1, 201-233 (1994; Zbl 0810.34007).] The applications of the Mellin transformation to the theory of linear differential and difference equations with polynomial coefficients in the case that the linear differential equation has a regular singularity at \(\infty\) and an irregular one at the origin of the complex plane, are studied. Two fundamental systems of solutions of an associated difference equation with the same asymptotic representation as the variable tends to \(\infty\), one in the right half plane and the other in the left half plane, are constructed.
linear differential and difference equations with polynomial coefficients
scientific article; zbMATH DE number 895809