Formula:7727

Digital Library of Mathematical Functions ID 22.11.E10

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \Jacobielldck@{z}{k}-\frac{\pi}{2K}\sec@@{\zeta}=\frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{2n+1}\cos@{(2n+1)\zeta}}{1-q^{2n+1}},}

Symbols List

• ${\displaystyle{\displaystyle\operatorname{dc}\left(\NVar{z},\NVar{k}\right)}}$: Jacobian elliptic 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
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle q}}$: nome
• ${\displaystyle{\displaystyle\sec\NVar{z}}}$: secant function
• ${\displaystyle{\displaystyle z}}$: complex
• ${\displaystyle{\displaystyle k}}$: modulus
• ${\displaystyle{\displaystyle\zeta}}$: change of variable
 

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