Formula:7819

Digital Library of Mathematical Functions ID 22.16.E7

${\displaystyle{\displaystyle\operatorname{am}\left(x,k\right)=x-\tfrac{1}{4}k^{2}(x-\sin x\cos x)+O\left(k^{4}\right),}}$

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle\operatorname{am}\left(\NVar{x},\NVar{k}\right)}}$: Jacobi’s amplitude function
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle x}}$: real
• ${\displaystyle{\displaystyle k}}$: modulus
 

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