Formula:5300

Digital Library of Mathematical Functions ID 13.20.E14

${\displaystyle{\displaystyle\zeta\sqrt{\alpha^{2}-\zeta^{2}}+\alpha^{2}\operatorname{arcsin}\left(\frac{\zeta}{\alpha}\right)=\frac{X}{\mu}+\frac{2\kappa}{\mu}\operatorname{arctan}\left(\frac{x-2\kappa}{X}\right)-2\operatorname{arctan}\left(\frac{\kappa x-2\mu^{2}}{\mu X}\right),}}$

Constraint(s)

${\displaystyle{\displaystyle 2\kappa-2\sqrt{\kappa^{2}-\mu^{2}}\leq x\leq 2\kappa+2\sqrt{\kappa^{2}-\mu^{2}}}}$

Symbols List

• ${\displaystyle{\displaystyle\operatorname{arcsin}\NVar{z}}}$:
• ${\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}$:
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\alpha}}$: 13.20.E6
• ${\displaystyle{\displaystyle X}}$: 13.20.E7
 

Resources that cite this formula

No records found.