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Published April 1975 | public
Journal Article

On an infinite series of Abel occurring in the theory of interpolation


The purpose of this paper is to show that for a certain class of functions f which are analytic in the complex plane possibly minus (−∞, −1], the Abel series ! is convergent for all β>0. Its sum is an entire function of exponential type and can be evaluated in terms of f. Furthermore, it is shown that the Abel series of f for small β>0 approximates f uniformly in half-planes of the form Re(z) ⩾ − 1 + δ, δ>0. At the end of the paper some special cases are discussed.

Additional Information

© 1975 Published by Elsevier Inc. Under an Elsevier user license. Communicated by P. L. Butzer. Dedicated to Professor G. G. Lorentz on the occasion of his sixty-fifth birthday. Work on this paper was supported in part by NSF Grant 23392.

Additional details

August 19, 2023
October 18, 2023