Formelsammlung Mathematik: Identitäten: Entwicklung nach Sinuspotenzen

Zurück zu Identitäten

$\cos 2n\theta =1-\frac{(2n{)}^2}{2!}{\sin }^2\theta +\frac{(2n{)}^2((2n{)}^2-2^2)}{4!}{\sin }^4\theta -\frac{(2n{)}^2((2n{)}^2-2^2)((2n{)}^2-4^2)}{6!}{\sin }^6\theta +...$

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$\cos 2\alpha \theta =\sum _{n=0}^{\mathrm{\infty }}(-1{)}^n\frac{\alpha (\alpha -1+n)!}{(\alpha -n)!}\frac{(2\sin \theta {)}^{2n}}{(2n)!}\alpha \in ℂ\setminus \mathbb{Z},\theta \in ]-\frac{\pi }{2},\frac{\pi }{2}[$

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$\sin px=\sum _{n=0}^{\mathrm{\infty }}(-1{)}^n{2}^{2n}p\frac{(\frac{p}{2}-\frac{1}{2}+n)!}{(\frac{p}{2}-\frac{1}{2}-n)!}\frac{(\sin x{)}^{2n+1}}{(2n+1)!}-\frac{\pi }{2}<x<\frac{\pi }{2},p\in ℂ$

Blender3D: Vorlage:Klappbox

$\cos px=\sum _{n=0}^{\mathrm{\infty }}(-1{)}^n{2}^{2n-1}p\frac{(\frac{p}{2}-1+n)!}{(\frac{p}{2}-n)!}\frac{(\sin x{)}^{2n}}{(2n)!}-\frac{\pi }{2}<x<\frac{\pi }{2},p\in ℂ$