Central factorial numbers; their main properties and some applications.

Abstract 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.