DLMF:14.15.E28 (Q4876)

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Language	Label	Description	Also known as
English	DLMF:14.15.E28	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\frac{1}{2}\alpha^{2}\operatorname{arcsin}\left(% \frac{\zeta}{\alpha}\right)+\frac{1}{2}\zeta\left(\alpha^{2}-\zeta^{2}\right)^% {1/2}=\operatorname{arcsin}\left(\frac{x}{a}\right)-\left(1-a^{2}\right)^{1/2}% \operatorname{arctan}\left(x\left(\frac{1-a^{2}}{a^{2}-x^{2}}\right)^{1/2}% \right),}}

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DLMF:14.15.E28

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{\displaystyle{\displaystyle-\alpha\leq\zeta\leq\alpha}}

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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.m7aadec

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Defining formula

{\displaystyle{\displaystyle x}}

C14.S1.XMD1.m1rdec

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Defining formula

{\displaystyle{\displaystyle a}}

C14.S15.XMD13.m1ddec

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Defining formula

{\displaystyle{\displaystyle\zeta}}

C14.S15.XMD14.m1cdec

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Defining formula

{\displaystyle{\displaystyle\alpha}}

C14.S15.XMD9.m1kdec

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