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

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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	$m\in {\mathbb {Z} },n\in {\mathbb {R} }$	$m\in {\mathbb {Z} },n\in {\mathbb {R} }$	$m\in {\mathbb {Z} },n\in {\mathbb {R} }$	$m\in {\mathbb {Z} },n\in {\mathbb {R} }$	$m\in {\mathbb {Z} },n\in {\mathbb {R} }$	$m\in {\mathbb {Z} },n\in {\mathbb {R} }$	$m\in {\mathbb {Z} },n\in {\mathbb {R} }$

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	$m\in {\mathbb {Z} },n\in {\mathbb {R} }$	$m\in {\mathbb {Z} },n\in {\mathbb {R} }$	$m\in {\mathbb {Z} },n\in {\mathbb {R} }$	$m\in {\mathbb {Z} },n\in {\mathbb {R} }$	$m\in {\mathbb {Z} },n\in {\mathbb {R} }$	$m\in {\mathbb {Z} },n\in {\mathbb {R} }$	$n\in {\mathbb {R} }$

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
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