Formula:7729

Digital Library of Mathematical Functions ID 22.11.E12

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

Symbols List

• ${\displaystyle{\displaystyle\operatorname{sc}\left(\NVar{z},\NVar{k}\right)}}$: 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
• ${\displaystyle{\displaystyle q}}$: nome
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle\tan\NVar{z}}}$: tangent function
• ${\displaystyle{\displaystyle z}}$: complex
• ${\displaystyle{\displaystyle k}}$: modulus
• ${\displaystyle{\displaystyle k^{\prime}}}$: complementary modulus
• ${\displaystyle{\displaystyle\zeta}}$: change of variable
 

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