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
Andrea Ossicini. The special function ش. Kragujevac Journal of Mathematics, Tome 27 (2005), p. 63 . http://geodesic.mathdoc.fr/item/KJM_2005_27_a6/
@article{KJM_2005_27_a6,
author = {Andrea Ossicini},
title = {The special function ش},
journal = {Kragujevac Journal of Mathematics},
pages = {63 },
year = {2005},
volume = {27},
language = {en},
url = {http://geodesic.mathdoc.fr/item/KJM_2005_27_a6/}
}