Geodesic
The special function ش
Kragujevac Journal of Mathematics, Tome 27 (2005), p. 63 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

THE SPECIAL FUNCTION Andrea OssiciniTELECOM -Italia, Via delle Azzorre 352-D2, 00121 Roma, Italy (e-mail: a.ossicini@finsiel.it)(Received March 12, 2005)Abstract. The purpose of the work is to furnish a study of a discrete and special function, discovered by the author and named with the Arabian letter (Shin), produced by a family of functions. A fundamental theorem is enunciated: it connects the rational values of this family with a natural number; to this aim two rational-value functions will be created, with the characteristic, in the field of real positive numbers, to be piecewise continuous. We state not only the existence of a separation element, but we prove that this element is just formed by one only integer constant function, the value of which is equal to 2. We point out a hypothetical, subtle connection among the special function , the Eulerian function Gamma and the second-order Eulerian numbers. It is finally proved that is completely monotonic: this characteristic is peculiar for the functions that have considerable applications in different fields of pure and applied Mathematics.
Keywords: special functions, gamma function, hypergeometric series, second-order Eulerian numbers, completely monotonic functions, integral transforms 
@article{KJM_2005_27_a6,
     author = {Andrea Ossicini},
     title = {The special function ش},
     journal = {Kragujevac Journal of Mathematics},
     pages = {63 },
     publisher = {mathdoc},
     volume = {27},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2005_27_a6/}
}
TY  - JOUR
AU  - Andrea Ossicini
TI  - The special function ش
JO  - Kragujevac Journal of Mathematics
PY  - 2005
SP  - 63 
VL  - 27
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KJM_2005_27_a6/
LA  - en
ID  - KJM_2005_27_a6
ER  - 
%0 Journal Article
%A Andrea Ossicini
%T The special function ش
%J Kragujevac Journal of Mathematics
%D 2005
%P 63 
%V 27
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KJM_2005_27_a6/
%G en
%F KJM_2005_27_a6
Andrea Ossicini. The special function ش. Kragujevac Journal of Mathematics, Tome 27 (2005), p. 63 . http://geodesic.mathdoc.fr/item/KJM_2005_27_a6/