Formula:6973

Digital Library of Mathematical Functions ID 19.11.E5

${\displaystyle{\displaystyle\Pi\left(\theta,\alpha^{2},k\right)+\Pi\left(\phi,\alpha^{2},k\right)=\Pi\left(\psi,\alpha^{2},k\right)-\alpha^{2}R_{C}\left(\gamma-\delta,\gamma\right),}}$

Symbols List

• ${\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}$: Carlson’s combination of inverse circular and inverse hyperbolic functions
• ${\displaystyle{\displaystyle\Pi\left(\NVar{\phi},\NVar{\alpha}^{2},\NVar{k}\right)}}$: Legendre’s incomplete elliptic integral of the third kind
• ${\displaystyle{\displaystyle\phi}}$: real or complex argument
• ${\displaystyle{\displaystyle k}}$: real or complex modulus
• ${\displaystyle{\displaystyle\alpha^{2}}}$: real or complex parameter
• ${\displaystyle{\displaystyle\theta}}$: amplitude
• ${\displaystyle{\displaystyle\psi}}$: angle
• ${\displaystyle{\displaystyle\gamma}}$: γ
• ${\displaystyle{\displaystyle\delta}}$: δ
 

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