q-analog meaning in French

q-analogue

In mathematics, a q-analog of a theorem, identity or expression is a generalization involving a new parameter q that returns the original theorem, identity or expression in the limit as q → 1.
En mathématiques, plus précisément dans le domaine de la combinatoire, un q-analogue d'un théorème, d'une identité ou d'une expression est une généralisation impliquant un nouveau paramètre q et qui se spécialise en le théorème originel lorsque l'on prend la limite quand q tend vers 1.
The equality lim q → 1 1 − q n 1 − q = n {\displaystyle \lim _{q\rightarrow 1}{\frac {1-q^{n}}{1-q}}=n} suggests that we define the q-analog of n, also known as the q-bracket or q-number of n, to be q = 1 − q n 1 − q = 1 + q + q 2 + … + q n − 1 . {\displaystyle _{q}={\frac {1-q^{n}}{1-q}}=1+q+q^{2}+\ldots +q^{n-1}.} By itself, the choice of this particular q-analog among the many possible options is unmotivated.
L'égalité lim q → 1 1 − q n 1 − q = n
The equality lim q → 1 1 − q n 1 − q = n {\displaystyle \lim _{q\rightarrow 1}{\frac {1-q^{n}}{1-q}}=n} suggests that we define the q-analog of n, also known as the q-bracket or q-number of n, to be q = 1 − q n 1 − q = 1 + q + q 2 + … + q n − 1 . {\displaystyle _{q}={\frac {1-q^{n}}{1-q}}=1+q+q^{2}+\ldots +q^{n-1}.} By itself, the choice of this particular q-analog among the many possible options is unmotivated.
L'égalité lim q → 1 1 − q n 1 − q = n