Formula:5325

Digital Library of Mathematical Functions ID 13.21.E20

${\displaystyle{\displaystyle\widehat{\zeta}=-\left(\frac{3}{2\kappa}\left(-\frac{1}{2}X+2\mu\operatorname{arctan}\left(\frac{x\kappa-x\sqrt{\kappa^{2}-\mu^{2}}-2\mu^{2}}{\mu X}\right)+\kappa\operatorname{arccos}\left(\frac{x-2\kappa}{2\sqrt{\kappa^{2}-\mu^{2}}}\right)\right)\right)^{2/3},}}$

Constraint(s)

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

Symbols List

• ${\displaystyle{\displaystyle\operatorname{arccos}\NVar{z}}}$:
• ${\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}$:
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle X}}$: 13.21.E18
 

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