2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139956The purpose of the work is to furnish a complete study of a discrete and special function, discovered by the author and named with the Arabian letter "SHIN" {The letter SHIN is the thirteenth letter of the Arabian alphabet}. It includes three other papers, published in the International journal "Kragujevac Journal of Mathematics". The methods, the techniques and the style of the demonstration inside such a work, are all related to Leonhard Euler, the very great Swiss mathematician.46 pages, 15 figuresGeneral Mathematics33B10;33B15;26A48text