I know that
\documentclass{article}
\usepackage{mathrsfs}
\usepackage{extarrows}
\begin{document}
$\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
\end{document}
produce :

but I want to know what is the necessary command to get :
I know that
\documentclass{article}
\usepackage{mathrsfs}
\usepackage{extarrows}
\begin{document}
$\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
\end{document}
produce :

but I want to know what is the necessary command to get :
\mathscr will give script fonts in math-mode only for upper cased letters; the shape will depend on the package used. As far as I know, there's no font providing this kind of fonts for lower-cased letters in math-mode. Don't use \mathscr to write regular, non-math text (it's intended to be used in math expressions).
In text mode, you can use the calligra font, provided by the calligra package:
\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{calligra}
\begin{document}
\normalfont\calligra
ABCDEFGHIJ\par
KLMNOPQRST\par
UVWXYZ
abcdefghijklmnopqrstuvwxyz
I like mathematics. Mathematics is a language.
\end{document}

Another option would be to use XeLaTeX and a font like the one in the image.
scris not used for texts. Don't use it to write words. – Sigur Aug 25 '13 at 00:52