Formula:7773

Digital Library of Mathematical Functions ID 22.14.E5

${\displaystyle{\displaystyle\int\operatorname{sd}\left(x,k\right)\mathrm{d}x=(kk^{\prime})^{-1}\operatorname{Arcsin}\left(-k\operatorname{cd}\left(x,k\right)\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\operatorname{cd}\left(\NVar{z},\NVar{k}\right)}}$: Jacobian elliptic function
• ${\displaystyle{\displaystyle\operatorname{sd}\left(\NVar{z},\NVar{k}\right)}}$: Jacobian elliptic function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\operatorname{Arcsin}\NVar{z}}}$: general arcsine function
• ${\displaystyle{\displaystyle x}}$: real
• ${\displaystyle{\displaystyle k}}$: modulus
• ${\displaystyle{\displaystyle k^{\prime}}}$: complementary modulus
 

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