Formula:7821

Digital Library of Mathematical Functions ID 22.16.E9

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \Jacobiamk@{x}{k}=\frac{\pi}{2K}x+2\sum_{n=1}^{\infty}\frac{q^{n}\sin@{2n\zeta}}{n(1+q^{2n})}.}

Symbols List

• ${\displaystyle{\displaystyle\operatorname{am}\left(\NVar{x},\NVar{k}\right)}}$: Jacobi’s amplitude function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle K\left(\NVar{k}\right)}}$: Legendre’s complete elliptic integral of the first kind
• ${\displaystyle{\displaystyle q}}$: nome
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle x}}$: real
• ${\displaystyle{\displaystyle k}}$: modulus
 

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