Recherche:Techniques de régressions au plus près/Fonctions régressives Fi communes de base

Début de la boite de navigation du chapitre

fin de la boite de navigation du chapitre

Fonctions régressives Fi communes de base

Dans les approches B et C

Fonctions paires pour partie paire

Fonctions régressives de base paires

Type F(x) Degré	Monôme	Cosinus trigonométrique	Tangente trigonométrique	Cosinus hyperbolique	Tangente hyperbolique	Exponentielle	Construite avec $f(x)$
0 1 -1	$1$	$1-\cos (\omega x)$ $1-{\cos }^{-1}(\omega x)$ $1-\cos (\omega x^{-1})$ $1-{\cos }^{-1}(\omega x^{-1})$ $1-\cos (\omega x^2)$ $1-{\cos }^{-1}(\omega x^2)$	$\tan (\omega x^2)$ ${\tan }^{-1}(\omega x^2)$ $\tan (\omega x^{-2})$ ${\tan }^{-1}(\omega x^{-2})$	$1-\cosh (\omega x)$ $1-{\cosh }^{-1}(\omega x)$ $1-\cosh (\omega x^{-1}$ $1-{\cosh }^{-1}(\omega x-1)$ $1-\cos (\omega x^2)$ $1-{\cos }^{-1}(\omega x^2)$	$\tanh (\omega x^2)$ ${\tanh }^{-1}(\omega x^2)$ $\tanh (\omega x^{-2})$ ${\tanh }^{-1}(\omega x^{-2})$	$1-\exp (\omega x^2)$ $1-{\exp }^{-1}(\omega x^2)$ $1-\exp (\omega x^2)$ $1-{\exp }^{-1}(\omega x^2)$	$F(x)=f(0)-f(x)$ si x>0 ET $F(x)=f(0)-f(-x)$ si x<0
2	$x^2$ $x^{-2}$	$1-{\cos }^2(\omega x)$ $1-{\cos }^{-2}(\omega x)$ $1-{\cos }^2(\omega x^{-1})$ $1-{\cos }^{-2}(\omega x^{-1})$	${\tan }^2(\omega x)$ ${\tan }^{-2}(\omega wx)$ ${\tan }^2(\omega x^{-1})$ ${\tan }^{-2}(\omega x^{-1})$	$1-{\cosh }^2(\omega x)$ $1-{\cosh }^{-2}(\omega x)$ $1-{\cosh }^2(\omega x^{-1})$ $1-{\cosh }^{-2}(\omega x^{-1})$	${\tanh }^2(\omega x)$ ${\tanh }^{-2}(\omega wx)$ ${\tanh }^2(\omega x^{-1})$ ${\tanh }^{-2}(\omega x^{-1})$	$1-{\exp }^2(\omega x)$ $1-{\exp }^{-2}(\omega x)$ $1-{\exp }^2(\omega x^{-1})$ $1-{\exp }^{-2}(\omega x^{-1})$	$F(x)=f(0)-f^2(x)$ si x>0 ET $F(x)=f^2(0)-f^2(-x)$ si x<0
n m	$x^{2n}$ $x^{-2n}$	$1-{\cos }^n(\omega x)$ $1-\cos (\omega x^m)$ $1-{\cos }^n(\omega x^m)$	${\tan }^{2n}(\omega x)$ ${\tan }^{-2n}(\omega x)$ ${\tan }^{2n}(\omega x^m)$	$1-{\cosh }^n(\omega x)$ $1-\cosh (\omega x^m)$ $1-{\cosh }^n(\omega x^m)$	${\tanh }^{2n}(\omega x)$ ${\tanh }^{-2n}(\omega x)$ ${\tanh }^{2n}(\omega x^m)$	$1-{\exp }^n(\omega x^{2m})$ $1-{\exp }^n(-\omega x^{2m})$	$F(x)=f(0)-f^n(x^{2m})$ si x>0 ET $F(x)=f^n(0)-f^n(-x^{2m})$ si x<0
général	$m\in \mathbb{Z},n\in ℝ$	$m\in \mathbb{Z},n\in ℝ$	$m\in \mathbb{Z},n\in ℝ$	$m\in \mathbb{Z},n\in ℝ$	$m\in \mathbb{Z},n\in ℝ$	$m\in \mathbb{Z},n\in ℝ$	$m\in \mathbb{Z},n\in ℝ$

Fonctions régressives composées paires

À FINIR 3 premières cellules faites

Type
MonômeAVEC Sin Cos Sinh Cosh Tan Tanh Exp	$x^{2l/2l+1}\times {\sin }^{2m/2m+1}(\omega x)$ XXXXXXXXXXXXXXXXXXXXXXXX $x^{2l/2l+1}\times {\sinh }^{2m/2m+1}(\omega x)$ XXXXXXXXXXXXXXXXXXXXXXXX $x^{2l/2l+1}\times {\tan }^{2m/2m+1}(\omega x)$ $x^{2l/2l+1}\times {\tanh }^{2m/2m+1}(\omega x)$ XXXXXXXXXXXXXXXXXXXXXXXX	$x^{2l}\times {\sin }^m(\omega x^2)$ $x^{2l}\times {\cos }^m(\omega x^2)$ $x^{2l}\times {\sinh }^m(\omega x^2)$ $x^{2l}\times {\cosh }^m(\omega x^2)$ $x^{2l}\times {\tan }^m(\omega x^2)$ $x^{2l}\times {\tanh }^m(\omega x^2)$ $x^{2l}\times {\exp }^m(\omega x^2)$	$x^{2l}\times {\sin }^{2m}(\omega x)$ $x^{2l}\times {\cos }^m(\omega x)$ $x^{2l}\times {\sinh }^{2m}(\omega x)$ $x^{2l}\times {\cos }^m(\omega x)$ $x^{2l}\times {\tan }^{2m}(\omega x)$ $x^{2l}\times {\tanh }^{2m}(\omega x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX	$x^{2l+1}\times {\sin }^{2m}(\omega x^{2n+1})$/$x^{2l+1}\times {\sin }^m(\omega x^{2n})$/$x^{2l}\times {\sin }^{2m+1}(\omega x^{2n+1})$ $x^{2l+1}\times {\cos }^{2m}(\omega x^{2n+1})$/$x^{2l+1}\times {\cos }^m(\omega x^{2n})$/XXXXXXXXXXXXXXXXXXXXXXXXXXXX $x^{2l+1}\times {\sinh }^{2m}(\omega x^{2n+1})$/$x^{2l+1}\times {\sinh }^m(\omega x^{2n})$/$x^{2l}\times {\sinh }^{2m+1}(\omega x^{2n+1})$ $x^{2l+1}\times {\cosh }^{2m}(\omega x^{2n+1})$/$x^{2l+1}\times {\cosh }^m(\omega x^{2n})$/XXXXXXXXXXXXXXXXXXXXXXXXXXXX $x^{2l+1}\times {\tan }^{2m+1}(\omega x^{2n+1})$/$x^{2l+1}\times {\tan }^m(\omega x^{2n})$/$x^{2l}\times {\tan }^{2m+1}(\omega x^{2n+1})$ $x^{2l+1}\times {\tanh }^{2m}(\omega x^{2n+1})$/$x^{2l+1}\times {\tanh }^m(\omega x^{2n})/x^{2l}\times {\tanh }^{2m+1}(\omega x^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXX /$x^{2l+1}\times {\exp }^m(\omega x^{2n})$/ XXXXXXXXXXXXXXXXXXXXXXXXXXXX
SinusAVEC Sin Cos Sinh Cosh Tan Tanh Exp	$\sin ({\omega }_{1}x)\times {\sin }^{2m}({\omega }_{2}x)$ $\sin ({\omega }_{1}x)\times {\cos }^m({\omega }_{2}x)$ $\sin ({\omega }_{1}x)\times {\sinh }^{2m}({\omega }_{2}x)$ $\sin ({\omega }_{1}x)\times {\cosh }^m({\omega }_{2}x)$ $\sin ({\omega }_{1}x)\times {\tan }^{2m}({\omega }_{2}x)$ $\sin ({\omega }_{1}x)\times {\tanh }^{2m}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXX	$\sin ({\omega }_1{x}^{2l+1})\times {\sin }^m(\omega x^2)$ $\sin ({\omega }_1{x}^{2l+1})\times {\cos }^m(\omega x^2)$ $\sin ({\omega }_1{x}^{2l+1})\times {\sinh }^m(\omega x^2)$ $\sin ({\omega }_1{x}^{2l+1})\times {\cosh }^m(\omega x^2)$ $\sin ({\omega }_1{x}^{2l+1})\times {\tan }^m(\omega x^2)$ $\sin ({\omega }_1{x}^{2l+1})\times {\tanh }^m(\omega x^2)$ $\sin ({\omega }_1{x}^{2l+1})\times {\exp }^m(\omega x^2)$	$\sin ({\omega }_1{x}^{2l})\times {\sin }^{2m+1}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX $\sin ({\omega }_1{x}^{2l})\times {\sinh }^{2m+1}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX $\sin ({\omega }_1{x}^{2l})\times {\tan }^{2m+1}({\omega }_{2}x)$ $\sin ({\omega }_1{x}^{2l})\times {\tanh }^{2m+1}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX	$\sin ({\omega }_1{x}^{2l+1})\times {\sin }^{2m}({\omega }_2{x}^{2n+1})$/$\sin ({\omega }_1{x}^{2l+1})\times {\sin }^m({\omega }_2{x}^{2n})$/$\sin ({\omega }_1{x}^{2l})\times {\sin }^{2m+1}({\omega }_2{x}^{2n+1})$ $\sin ({\omega }_1{x}^{2l+1})\times {\cos }^{2m}({\omega }_2{x}^{2n+1})$/${\omega }_{1}sin(x^{2l+1})\times {\cos }^m({\omega }_2{x}^{2n})$/XXXXXXXXXXXXXXXXXXXXXXXXXXXX $\sin ({\omega }_1{x}^{2l+1})\times {\sinh }^{2m}({\omega }_2{x}^{2n+1})$/$\sin ({\omega }_1{x}^{2l+1})\times {\sinh }^m({\omega }_2{x}^{2n})$/$\sin ({\omega }_1{x}^{2l})\times {\sinh }^{2m+1}({\omega }_2{x}^{2n+1})$ $\sin ({\omega }_1{x}^{2l+1})\times {\cosh }^{2m}({\omega }_2{x}^{2n+1})$/$\sin ({\omega }_1{x}^{2l+1})\times {\cosh }^m({\omega }_2{x}^{2n})$/ XXXXXXXXXXXXXXXXXXX $\sin ({\omega }_1{x}^{2l+1})\times {\tan }^{2m}({\omega }_2{x}^{2n+1})$/$\sin ({\omega }_1{x}^{2l+1})\times {\tan }^m({\omega }_2{x}^{2n})$/$\sin ({\omega }_1{x}^{2l})\times {\tan }^{2m+1}({\omega }_2{x}^{2n+1})$ $\sin ({\omega }_1{x}^{2l+1})\times {\tanh }^{2m}({\omega }_2{x}^{2n+1})$/$\sin ({\omega }_1{x}^{2l+1})\times {\tanh }^m({\omega }_2{x}^{2n})/\sin ({\omega }_1{x}^{2l})\times {\tanh }^{2m+1}({\omega }_2{x}^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXX/$\sin ({\omega }_1{x}^{2l+1})\times {\exp }^m({\omega }_2{x}^{2n})$/XXXXXXXXXXXXXXXXXXXXXXXXXXXX
Cos AVEC Cos Sinh Cosh Tan Tanh Exp	XXXXXXXXXXXXXXXXXXXXXXXX $\cos ({\omega }_{1}x)\times {\sinh }^{2m+1}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXX $\cos ({\omega }_{1}x)\times {\tan }^{2m+1}({\omega }_{2}x)$ $\cos ({\omega }_{1}x)\times {\tanh }^{2m+1}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXX	XXXXXXXXXXXXXXXXXXXXXXXXXXXX $\cos ({\omega }_1{x}^l)\times {\sinh }^{2m+1}(\omega x^2)$ XXXXXXXXXXXXXXXXXXXXXXXXXXXX $\cos ({\omega }_1{x}^l)\times {\tan }^{2m+1}(\omega x^2)$ $\cos ({\omega }_1{x}^l)\times {\tanh }^{2m+1}(\omega x^2)$ XXXXXXXXXXXXXXXXXXXXXXXXXXXX	XXXXXXXXXXXXXXXXXXXXXXXXXXX $\cos ({\omega }_1{x}^l)\times {\sinh }^{2m+1}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX $\cos ({\omega }_1{x}^l)\times {\tan }^{2m+1}({\omega }_{2}x)$ $\cos ({\omega }_1{x}^l)\times {\tanh }^{2m+1}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX	XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX $\cos ({\omega }_1{x}^{2l+1})\times {\sinh }^{2m+1}({\omega }_2{x}^{2n+1})$/$\cos ({\omega }_1{x}^{2l+1})\times {\sinh }^{2m+1}({\omega }_2{x}^{2n})$/$\cos ({\omega }_1{x}^{2l})\times {\sinh }^{2m+1}({\omega }_2{x}^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX $\cos ({\omega }_1{x}^{2l+1})\times {\tan }^{2m+1}({\omega }_2{x}^{2n+1})$/$\cos ({\omega }_1{x}^{2l+1})\times {\tan }^{2m+1}({\omega }_2{x}^{2n})$/$\cos ({\omega }_1{x}^{2l})\times {\tan }^{2m+1}({\omega }_2{x}^{2n+1})$ $\cos ({\omega }_1{x}^{2l+1})\times {\tanh }^{2m+1}({\omega }_2{x}^{2n+1})$/$\cos ({\omega }_1{x}^{2l+1})\times {\tanh }^{2m+1}({\omega }_2{x}^{2n})/\cos ({\omega }_1{x}^{2l})\times {\tanh }^{2m+1}({\omega }_2{x}^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
Cosh AVEC Sinh Cosh Tan Tanh Exp	$\cosh ({\omega }_{1}x)\times {\sinh }^{2m+1}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXX $\cosh ({\omega }_{1}x)\times {\tan }^{2m+1}({\omega }_{2}x)$ $\cosh ({\omega }_{1}x)\times {\tanh }^{2m+1}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXX	$\cosh ({\omega }_1{x}^l)\times {\sinh }^{2m+1}(\omega x^2)$ XXXXXXXXXXXXXXXXXXXXXXXXXXXX $\cosh ({\omega }_1{x}^l)\times {\tan }^{2m+1}(\omega x^2)$ $\cosh ({\omega }_1{x}^l)\times {\tanh }^{2m+1}(\omega x^2)$ XXXXXXXXXXXXXXXXXXXXXXXXXXXX	$\cosh ({\omega }_1{x}^l)\times {\sinh }^{2m+1}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX $\cosh ({\omega }_1{x}^l)\times {\tan }^{2m+1}({\omega }_{2}x)$ $\cosh ({\omega }_1{x}^l)\times {\tanh }^{2m+1}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX	$\cosh ({\omega }_1{x}^{2l+1})\times {\sinh }^{2m+1}({\omega }_2{x}^{2n+1})$/$\cosh ({\omega }_1{x}^{2l+1})\times {\sinh }^{2m+1}({\omega }_2{x}^{2n})$/$\cosh ({\omega }_1{x}^{2l})\times {\sinh }^{2m+1}({\omega }_2{x}^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX $\cosh ({\omega }_1{x}^{2l+1})\times {\tan }^{2m+1}({\omega }_2{x}^{2n+1})$/$\cosh ({\omega }_1{x}^{2l+1})\times {\tan }^{2m+1}({\omega }_2{x}^{2n})$/$\cosh ({\omega }_1{x}^{2l})\times {\tan }^{2m+1}({\omega }_2{x}^{2n+1})$ $\cosh ({\omega }_1{x}^{2l+1})\times {\tanh }^{2m+1}({\omega }_2{x}^{2n+1})$/$\cosh ({\omega }_1{x}^{2l+1})\times {\tanh }^{2m+1}({\omega }_2{x}^{2n})/\cosh ({\omega }_1{x}^{2l})\times {\tanh }^{2m+1}({\omega }_2{x}^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
Tan AVEC Tan Tanh Exp	$\tan ({\omega }_{1}x)\times {\tan }^{2m}({\omega }_{2}x)$ $\tan ({\omega }_{1}x)\times {\tanh }^{2m}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXX	$\tan ({\omega }_1{x}^{2l+1})\times {\tan }^{2m+1}(\omega x^2)$ $\tan ({\omega }_1{x}^{2l+1})\times {\tanh }^{2m+1}(\omega x^2)$ $\tan ({\omega }_1{x}^{2l+1})\times {\exp }^m(\omega x^2)$	$\tan ({\omega }_1{x}^{2l})\times {\tan }^{2m+1}({\omega }_{2}x)$ $\tan ({\omega }_1{x}^{2l})\times {\tanh }^{2m+1}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX	$\tan ({\omega }_1{x}^{2l+1})\times {\tan }^{2m+1}({\omega }_2{x}^{2n+1})$/$\tan ({\omega }_1{x}^{2l+1})\times {\tan }^{2m+1}({\omega }_2{x}^{2n})$/$\tan ({\omega }_1{x}^{2l})\times {\tan }^{2m+1}({\omega }_2{x}^{2n+1})$ $\tan ({\omega }_1{x}^{2l+1})\times {\tanh }^{2m}({\omega }_2{x}^{2n+1})$/$\tan ({\omega }_1{x}^{2l+1})\times {\tanh }^{2m+1}({\omega }_2{x}^{2n})/\tan ({\omega }_1{x}^{2l})\times {\tanh }^{2m+1}({\omega }_2{x}^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
Tanh AVEC Tanh Exp	$\tanh ({\omega }_{1}x)\times {\tanh }^{2m}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXX	$\tanh ({\omega }_1{x}^{2l+1})\times {\tanh }^{2m+1}(\omega x^2)$ $\tanh ({\omega }_1{x}^{2l+1})\times {\exp }^m(\omega x^2)$	$\tanh ({\omega }_1{x}^{2l})\times {\tanh }^{2m+1}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX	$\tanh ({\omega }_1{x}^{2l+1})\times {\tanh }^{2m}({\omega }_2{x}^{2n+1})$/$\tanh ({\omega }_1{x}^{2l+1})\times {\tanh }^{2m+1}({\omega }_2{x}^{2n})/\tanh ({\omega }_1{x}^{2l})\times {\tanh }^{2m+1}({\omega }_2{x}^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX$\tan ({\omega }_1{x}^{2l+1})\times {\exp }^m(\omega x^2)$XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
Construite Approchée

Fonctions composées par 2 paires

AJOUTER TABLEAU DES COMBINéS

Fonctions impaires pour partie impaire

Fonctions de base

Type F(x) Degré	Monôme	Sinus trigonométrique	Tangente trigonométrique	Sinus hyperbolique	Tangente hyperbolique	Exponentielle	Construite avec $f(x)$
0 1 -1	$x$ $x^{-1}$	$\sin (\omega x)$ ${\sin }^{-1}(\omega x)$ $\sin (\omega x^{-1})$ ${\sin }^{-1}(\omega x^{-1})$	$\tan (\omega x)$ ${\tan }^{-1}(\omega x)$ $\tan (\omega x-1)$ ${\tan }^{-1}(\omega x-1)$	$\sinh (\omega x)$ ${\sinh }^{-1}(\omega x)$ $\sinh (\omega x^{-1})$ ${\sinh }^{-1}(\omega x^{-1})$	$\tanh (\omega x)$ ${\tanh }^{-1}(\omega x)$ $\tanh (\omega x-1)$ ${\tanh }^{-1}(\omega x-1)$	$-e^{\omega |x|}$ si x<0 ET $e^{\omega |x|}$ si x>0</math>	$F(x)=f(x)$ si x>0 ET $F(x)=-f(-x)$ si x<0
3	$x^3$ $x^{-3}$	${\sin }^3(\omega x)$ ${\sin }^{-3}(\omega x)$ ${\sin }^3(\omega x^{-1})$ ${\sin }^{-3}(\omega x-1)$	${\tan }^3(\omega x)$ ${\tan }^{-3}(\omega x)$ ${\tan }^3(\omega x-1)$ ${\tan }^{-3}(\omega x-1)$	${\sinh }^3(\omega x)$ ${\sinh }^{-3}(\omega x)$ ${\sinh }^3(\omega x-1)$ ${\sinh }^{-3}(\omega x-1)$	${\tanh }^3(\omega x)$ ${\tanh }^{-3}(\omega x)$ ${\tanh }^3(\omega x-1)$ ${\tanh }^{-3}(\omega x-1)$	$(-e^{\omega |x^3|}$ si x>0 ET $e^{\omega |x^3|}$ si x<0	$F(x)=f^2(x)$ si x>0 ET $F(x)=-f^2(-x)$ si x<0
2m+1 2n+1	$x^{2n+1}$ $x^{-(2n+1)}$	${\sin }^{2n+1}(\omega x^{2m+1})$ ${\sin }^{-(2n+1)}(\omega x^{2m+1})$	${\tan }^{2n+1}(\omega x^{2m+1})$ ${\tan }^{-(2n+1)}(\omega x^{2m+1})$	${\sinh }^{2n+1}(\omega x^{2m+1})$ ${\sinh }^{-(2n+1)}(\omega x^{2m+1})$	${\tanh }^{2n+1}(\omega x^{2m+1})$ ${\tanh }^{-(2n+1)}(\omega x^{2m+1})$	$-e^{\omega |x^{2m+1}|}$ si x>0 ET $e^{\omega |x^{2m+1}|}$ si x<0	$F(x)=f^n(x^{2m+1})$ si x>0 ET $F(x)=-f^n(-x^{2m+1})$ si x<0
général	$m\in \mathbb{Z},n\in ℝ$	$m\in \mathbb{Z},n\in ℝ$	$m\in \mathbb{Z},n\in ℝ$	$m\in \mathbb{Z},n\in ℝ$	$m\in \mathbb{Z},n\in ℝ$	$m\in \mathbb{Z},n\in ℝ$	$n\in ℝ$

Fonctions régressives composées impaires

Règles :

Tableau des parités d'un produit à à faire

Type	Degré i/p/i	Degré i/i_p/p	Degré p/i/i	Degré ipi/i-p/pii
MonômeAVEC Sin Cos Sinh Cosh Tan Tanh Exp	$x^{2l+1}\times {\sin }^{2m}(\omega x)$ $x^{2l+1}\times {\cos }^{2m}(\omega x)$ $x^{2l+1}\times {\sinh }^{2m}(\omega x)$ $x^{2l+1}\times {\cosh }^{2m}(\omega x)$ $x^{2l+1}\times {\tan }^{2m}(\omega x)$ $x^{2l+1}\times {\tanh }^{2m}(\omega x)$ XXXXXXXXXXXXXXXXXXXXXXXX	$x^{2l+1}\times {\sin }^m(\omega x^2)$ $x^{2l+1}\times {\cos }^m(\omega x^2)$ $x^{2l+1}\times {\sinh }^m(\omega x^2)$ $x^{2l+1}\times {\cosh }^m(\omega x^2)$ $x^{2l+1}\times {\tan }^m(\omega x^2)$ $x^{2l+1}\times {\tanh }^m(\omega x^2)$ $x^{2l+1}\times {\exp }^m(\omega x^2)$	$x^{2l}\times {\sin }^{2m+1}(\omega x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX $x^{2l}\times {\sinh }^{2m+1}(\omega x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX $x^{2l}\times {\tan }^{2m+1}(\omega x)$ $x^{2l}\times {\tanh }^{2m+1}(\omega x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX	$x^{2l+1}\times {\sin }^{2m}(\omega x^{2n+1})$/$x^{2l+1}\times {\sin }^m(\omega x^{2n})$/$x^{2l}\times {\sin }^{2m+1}(\omega x^{2n+1})$ $x^{2l+1}\times {\cos }^{2m}(\omega x^{2n+1})$/$x^{2l+1}\times {\cos }^m(\omega x^{2n})$/XXXXXXXXXXXXXXXXXXXXXXXXXXXX $x^{2l+1}\times {\sinh }^{2m}(\omega x^{2n+1})$/$x^{2l+1}\times {\sinh }^m(\omega x^{2n})$/$x^{2l}\times {\sinh }^{2m+1}(\omega x^{2n+1})$ $x^{2l+1}\times {\cosh }^{2m}(\omega x^{2n+1})$/$x^{2l+1}\times {\cosh }^m(\omega x^{2n})$/XXXXXXXXXXXXXXXXXXXXXXXXXXXX $x^{2l+1}\times {\tan }^{2m+1}(\omega x^{2n+1})$/$x^{2l+1}\times {\tan }^m(\omega x^{2n})$/$x^{2l}\times {\tan }^{2m+1}(\omega x^{2n+1})$ $x^{2l+1}\times {\tanh }^{2m}(\omega x^{2n+1})$/$x^{2l+1}\times {\tanh }^m(\omega x^{2n})/x^{2l}\times {\tanh }^{2m+1}(\omega x^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXX /$x^{2l+1}\times {\exp }^m(\omega x^{2n})$/ XXXXXXXXXXXXXXXXXXXXXXXXXXXX
SinusAVEC Sin Cos Sinh Cosh Tan Tanh Exp	$\sin ({\omega }_{1}x)\times {\sin }^{2m}({\omega }_{2}x)$ $\sin ({\omega }_{1}x)\times {\cos }^m({\omega }_{2}x)$ $\sin ({\omega }_{1}x)\times {\sinh }^{2m}({\omega }_{2}x)$ $\sin ({\omega }_{1}x)\times {\cosh }^m({\omega }_{2}x)$ $\sin ({\omega }_{1}x)\times {\tan }^{2m}({\omega }_{2}x)$ $\sin ({\omega }_{1}x)\times {\tanh }^{2m}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXX	$\sin ({\omega }_1{x}^{2l+1})\times {\sin }^m(\omega x^2)$ $\sin ({\omega }_1{x}^{2l+1})\times {\cos }^m(\omega x^2)$ $\sin ({\omega }_1{x}^{2l+1})\times {\sinh }^m(\omega x^2)$ $\sin ({\omega }_1{x}^{2l+1})\times {\cosh }^m(\omega x^2)$ $\sin ({\omega }_1{x}^{2l+1})\times {\tan }^m(\omega x^2)$ $\sin ({\omega }_1{x}^{2l+1})\times {\tanh }^m(\omega x^2)$ $\sin ({\omega }_1{x}^{2l+1})\times {\exp }^m(\omega x^2)$	$\sin ({\omega }_1{x}^{2l})\times {\sin }^{2m+1}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX $\sin ({\omega }_1{x}^{2l})\times {\sinh }^{2m+1}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX $\sin ({\omega }_1{x}^{2l})\times {\tan }^{2m+1}({\omega }_{2}x)$ $\sin ({\omega }_1{x}^{2l})\times {\tanh }^{2m+1}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX	$\sin ({\omega }_1{x}^{2l+1})\times {\sin }^{2m}({\omega }_2{x}^{2n+1})$/$\sin ({\omega }_1{x}^{2l+1})\times {\sin }^m({\omega }_2{x}^{2n})$/$\sin ({\omega }_1{x}^{2l})\times {\sin }^{2m+1}({\omega }_2{x}^{2n+1})$ $\sin ({\omega }_1{x}^{2l+1})\times {\cos }^{2m}({\omega }_2{x}^{2n+1})$/${\omega }_{1}sin(x^{2l+1})\times {\cos }^m({\omega }_2{x}^{2n})$/XXXXXXXXXXXXXXXXXXXXXXXXXXXX $\sin ({\omega }_1{x}^{2l+1})\times {\sinh }^{2m}({\omega }_2{x}^{2n+1})$/$\sin ({\omega }_1{x}^{2l+1})\times {\sinh }^m({\omega }_2{x}^{2n})$/$\sin ({\omega }_1{x}^{2l})\times {\sinh }^{2m+1}({\omega }_2{x}^{2n+1})$ $\sin ({\omega }_1{x}^{2l+1})\times {\cosh }^{2m}({\omega }_2{x}^{2n+1})$/$\sin ({\omega }_1{x}^{2l+1})\times {\cosh }^m({\omega }_2{x}^{2n})$/ XXXXXXXXXXXXXXXXXXX $\sin ({\omega }_1{x}^{2l+1})\times {\tan }^{2m}({\omega }_2{x}^{2n+1})$/$\sin ({\omega }_1{x}^{2l+1})\times {\tan }^m({\omega }_2{x}^{2n})$/$\sin ({\omega }_1{x}^{2l})\times {\tan }^{2m+1}({\omega }_2{x}^{2n+1})$ $\sin ({\omega }_1{x}^{2l+1})\times {\tanh }^{2m}({\omega }_2{x}^{2n+1})$/$\sin ({\omega }_1{x}^{2l+1})\times {\tanh }^m({\omega }_2{x}^{2n})/\sin ({\omega }_1{x}^{2l})\times {\tanh }^{2m+1}({\omega }_2{x}^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXX/$\sin ({\omega }_1{x}^{2l+1})\times {\exp }^m({\omega }_2{x}^{2n})$/XXXXXXXXXXXXXXXXXXXXXXXXXXXX
Cos AVEC Cos Sinh Cosh Tan Tanh Exp	XXXXXXXXXXXXXXXXXXXXXXXX $\cos ({\omega }_{1}x)\times {\sinh }^{2m+1}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXX $\cos ({\omega }_{1}x)\times {\tan }^{2m+1}({\omega }_{2}x)$ $\cos ({\omega }_{1}x)\times {\tanh }^{2m+1}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXX	XXXXXXXXXXXXXXXXXXXXXXXXXXXX $\cos ({\omega }_1{x}^l)\times {\sinh }^{2m+1}(\omega x^2)$ XXXXXXXXXXXXXXXXXXXXXXXXXXXX $\cos ({\omega }_1{x}^l)\times {\tan }^{2m+1}(\omega x^2)$ $\cos ({\omega }_1{x}^l)\times {\tanh }^{2m+1}(\omega x^2)$ XXXXXXXXXXXXXXXXXXXXXXXXXXXX	XXXXXXXXXXXXXXXXXXXXXXXXXXX $\cos ({\omega }_1{x}^l)\times {\sinh }^{2m+1}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX $\cos ({\omega }_1{x}^l)\times {\tan }^{2m+1}({\omega }_{2}x)$ $\cos ({\omega }_1{x}^l)\times {\tanh }^{2m+1}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX	XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX $\cos ({\omega }_1{x}^{2l+1})\times {\sinh }^{2m+1}({\omega }_2{x}^{2n+1})$/$\cos ({\omega }_1{x}^{2l+1})\times {\sinh }^{2m+1}({\omega }_2{x}^{2n})$/$\cos ({\omega }_1{x}^{2l})\times {\sinh }^{2m+1}({\omega }_2{x}^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX $\cos ({\omega }_1{x}^{2l+1})\times {\tan }^{2m+1}({\omega }_2{x}^{2n+1})$/$\cos ({\omega }_1{x}^{2l+1})\times {\tan }^{2m+1}({\omega }_2{x}^{2n})$/$\cos ({\omega }_1{x}^{2l})\times {\tan }^{2m+1}({\omega }_2{x}^{2n+1})$ $\cos ({\omega }_1{x}^{2l+1})\times {\tanh }^{2m+1}({\omega }_2{x}^{2n+1})$/$\cos ({\omega }_1{x}^{2l+1})\times {\tanh }^{2m+1}({\omega }_2{x}^{2n})/\cos ({\omega }_1{x}^{2l})\times {\tanh }^{2m+1}({\omega }_2{x}^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
Cosh AVEC Sinh Cosh Tan Tanh Exp	$\cosh ({\omega }_{1}x)\times {\sinh }^{2m+1}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXX $\cosh ({\omega }_{1}x)\times {\tan }^{2m+1}({\omega }_{2}x)$ $\cosh ({\omega }_{1}x)\times {\tanh }^{2m+1}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXX	$\cosh ({\omega }_1{x}^l)\times {\sinh }^{2m+1}(\omega x^2)$ XXXXXXXXXXXXXXXXXXXXXXXXXXXX $\cosh ({\omega }_1{x}^l)\times {\tan }^{2m+1}(\omega x^2)$ $\cosh ({\omega }_1{x}^l)\times {\tanh }^{2m+1}(\omega x^2)$ XXXXXXXXXXXXXXXXXXXXXXXXXXXX	$\cosh ({\omega }_1{x}^l)\times {\sinh }^{2m+1}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX $\cosh ({\omega }_1{x}^l)\times {\tan }^{2m+1}({\omega }_{2}x)$ $\cosh ({\omega }_1{x}^l)\times {\tanh }^{2m+1}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX	$\cosh ({\omega }_1{x}^{2l+1})\times {\sinh }^{2m+1}({\omega }_2{x}^{2n+1})$/$\cosh ({\omega }_1{x}^{2l+1})\times {\sinh }^{2m+1}({\omega }_2{x}^{2n})$/$\cosh ({\omega }_1{x}^{2l})\times {\sinh }^{2m+1}({\omega }_2{x}^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX $\cosh ({\omega }_1{x}^{2l+1})\times {\tan }^{2m+1}({\omega }_2{x}^{2n+1})$/$\cosh ({\omega }_1{x}^{2l+1})\times {\tan }^{2m+1}({\omega }_2{x}^{2n})$/$\cosh ({\omega }_1{x}^{2l})\times {\tan }^{2m+1}({\omega }_2{x}^{2n+1})$ $\cosh ({\omega }_1{x}^{2l+1})\times {\tanh }^{2m+1}({\omega }_2{x}^{2n+1})$/$\cosh ({\omega }_1{x}^{2l+1})\times {\tanh }^{2m+1}({\omega }_2{x}^{2n})/\cosh ({\omega }_1{x}^{2l})\times {\tanh }^{2m+1}({\omega }_2{x}^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
Tan AVEC Tan Tanh Exp	$\tan ({\omega }_{1}x)\times {\tan }^{2m}({\omega }_{2}x)$ $\tan ({\omega }_{1}x)\times {\tanh }^{2m}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXX	$\tan ({\omega }_1{x}^{2l+1})\times {\tan }^{2m+1}(\omega x^2)$ $\tan ({\omega }_1{x}^{2l+1})\times {\tanh }^{2m+1}(\omega x^2)$ $\tan ({\omega }_1{x}^{2l+1})\times {\exp }^m(\omega x^2)$	$\tan ({\omega }_1{x}^{2l})\times {\tan }^{2m+1}({\omega }_{2}x)$ $\tan ({\omega }_1{x}^{2l})\times {\tanh }^{2m+1}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX	$\tan ({\omega }_1{x}^{2l+1})\times {\tan }^{2m+1}({\omega }_2{x}^{2n+1})$/$\tan ({\omega }_1{x}^{2l+1})\times {\tan }^{2m+1}({\omega }_2{x}^{2n})$/$\tan ({\omega }_1{x}^{2l})\times {\tan }^{2m+1}({\omega }_2{x}^{2n+1})$ $\tan ({\omega }_1{x}^{2l+1})\times {\tanh }^{2m}({\omega }_2{x}^{2n+1})$/$\tan ({\omega }_1{x}^{2l+1})\times {\tanh }^{2m+1}({\omega }_2{x}^{2n})/\tan ({\omega }_1{x}^{2l})\times {\tanh }^{2m+1}({\omega }_2{x}^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
Tanh AVEC Tanh Exp	$\tanh ({\omega }_{1}x)\times {\tanh }^{2m}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXX	$\tanh ({\omega }_1{x}^{2l+1})\times {\tanh }^{2m+1}(\omega x^2)$ $\tanh ({\omega }_1{x}^{2l+1})\times {\exp }^m(\omega x^2)$	$\tanh ({\omega }_1{x}^{2l})\times {\tanh }^{2m+1}({\omega }_{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX	$\tanh ({\omega }_1{x}^{2l+1})\times {\tanh }^{2m}({\omega }_2{x}^{2n+1})$/$\tanh ({\omega }_1{x}^{2l+1})\times {\tanh }^{2m+1}({\omega }_2{x}^{2n})/\tanh ({\omega }_1{x}^{2l})\times {\tanh }^{2m+1}({\omega }_2{x}^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX$\tan ({\omega }_1{x}^{2l+1})\times {\exp }^m(\omega x^2)$XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
Construite Approchée