Formula:7780

Digital Library of Mathematical Functions ID 22.14.E12

${\displaystyle{\displaystyle\int\operatorname{cs}\left(x,k\right)\mathrm{d}x=\ln\left(\operatorname{ns}\left(x,k\right)-\operatorname{ds}\left(x,k\right)\right).}}$

Symbols List

• ${\displaystyle{\displaystyle\operatorname{cs}\left(\NVar{z},\NVar{k}\right)}}$: Jacobian elliptic function
• ${\displaystyle{\displaystyle\operatorname{ds}\left(\NVar{z},\NVar{k}\right)}}$: Jacobian elliptic function
• ${\displaystyle{\displaystyle\operatorname{ns}\left(\NVar{z},\NVar{k}\right)}}$: Jacobian elliptic function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle x}}$: real
• ${\displaystyle{\displaystyle k}}$: modulus
 

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