Interpolation by a sum of exponential functions when some exponents are preassigned

AbstractIn a recent paper (A. Sidi, J. Approx. Theory 34 (1982), 194–210) the author has given the solutions to the problems of interpolation at equidistant points and confluent interpolation by a sum of exponential functions when none of the exponents is known. In the present work we generalize these results by specifying some of the exponents. Necessary and sufficient conditions for existence and uniqueness of solutions are given, and the solutions are provided in closed form. The connection of these problems with Padé approximants is exploited to prove a limit result