Central factorial numbers; their main properties and some applications.

The purpose of this paper is to present a systematic treatment of central factorial numbers (cfn), including their main properties, as well as to employ them in a variety of applications. The cfn are related more closely to the Stirling numbers than to the other well-known numbers of Bernoulli, Euler, etc., and they are at least as important as Stirling's numbers, said to be “as important as Bernoulli's, or even more so”. ∗Regretably, Professor Stark, an ambitious and much-respected mathematician at Aachen, died suddenly on April 23, 1986, at the age of 46. This manuscript was announced under the authorship of Stark and Vogt in [22]. At his death, a first version of about 18 pages, in addition to Diplom-Arbeiten master theses) by Dr. Lothar Vogt [74] and Dip1.-Math. Verena Bebronne [5] supervised by Stark, represented the initial stage of this work. Prof. Butzer and Dr. Vogt continued work on this paper in the winter of 1987, and were joined by Dip1.-Math. Schmidt in the spring of 1988. ∗∗Institut für Reine und Angewandte Mathematik, Aachen; since Oct. 1, 1987 at Blaupunkt-Verke GmbH, Robert-Bosch-Str. 200, 3200 Hildesheim. ∗Regretably, Professor Stark, an ambitious and much-respected mathematician at Aachen, died suddenly on April 23, 1986, at the age of 46. This manuscript was announced under the authorship of Stark and Vogt in [22]. At his death, a first version of about 18 pages, in addition to Diplom-Arbeiten master theses) by Dr. Lothar Vogt [74] and Dip1.-Math. Verena Bebronne [5] supervised by Stark, represented the initial stage of this work. Prof. Butzer and Dr. Vogt continued work on this paper in the winter of 1987, and were joined by Dip1.-Math. Schmidt in the spring of 1988. ∗∗Institut für Reine und Angewandte Mathematik, Aachen; since Oct. 1, 1987 at Blaupunkt-Verke GmbH, Robert-Bosch-Str. 200, 3200 Hildesheim. Notes ∗Regretably, Professor Stark, an ambitious and much-respected mathematician at Aachen, died suddenly on April 23, 1986, at the age of 46. This manuscript was announced under the authorship of Stark and Vogt in [22]. At his death, a first version of about 18 pages, in addition to Diplom-Arbeiten master theses) by Dr. Lothar Vogt [74] and Dip1.-Math. Verena Bebronne [5] supervised by Stark, represented the initial stage of this work. Prof. Butzer and Dr. Vogt continued work on this paper in the winter of 1987, and were joined by Dip1.-Math. Schmidt in the spring of 1988. ∗∗Institut für Reine und Angewandte Mathematik, Aachen; since Oct. 1, 1987 at Blaupunkt-Verke GmbH, Robert-Bosch-Str. 200, 3200 Hildesheim.