Remarks on exponential splines,in particular a contour integral representation of exponential B-splines

In the present paper we consider spline functions which are piecewise exponential sums of the form Σ α_μe^μx. Using the notation of Schumaker 10], we construct recursively computable B-splines of this space, where we make use of a complex contour integral. Furthermore, it is shown that this definition of a B-spline coincides in a certain sense with the ‘usual’ ones. which are based on the concept of generalized divided differences (e.g. 3, 12]). Finally, some additional properties of exponential B-splines are presented, including a differential relation.