DLMF:13.20.E14 (Q4603): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:13.20.E14	No description defined

Statements

Defining formula

{\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),}}

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DLMF:13.20.E14

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

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Defining formula

{\displaystyle{\displaystyle\operatorname{arcsin}\NVar{z}}}

C4.S23.SS2.p1.m5adec

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Defining formula

{\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}

C4.S23.SS2.p1.m7adec

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Defining formula

{\displaystyle{\displaystyle x}}

C13.S1.XMD4.m1kdec

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Defining formula

{\displaystyle{\displaystyle\alpha}}

C13.S20.XMD2.m1cdec

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