DLMF:14.15.E27 (Q4875): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:14.15.E27	No description defined

Statements

Defining formula

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

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DLMF:14.15.E27

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{\displaystyle{\displaystyle\alpha\leq\zeta<\infty}}

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Defining formula

{\displaystyle{\displaystyle\operatorname{arccosh}\NVar{z}}}

C4.S37.SS2.p1.m9adec

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Defining formula

{\displaystyle{\displaystyle\operatorname{arctanh}\NVar{z}}}

C4.S37.SS2.p1.m10adec

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Defining formula

{\displaystyle{\displaystyle x}}

C14.S1.XMD1.m1qdec

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Defining formula

{\displaystyle{\displaystyle a}}

C14.S15.XMD13.m1cdec

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