DLMF:14.15.E31 (Q4879)

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Language	Label	Description	Also known as
English	DLMF:14.15.E31	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{arcsinh}\left(\frac{\zeta}{\alpha}% \right)=\left(1+a^{2}\right)^{1/2}\operatorname{arctanh}\left(x\left(\frac{1+a% ^{2}}{x^{2}+a^{2}}\right)^{1/2}\right)-\operatorname{arcsinh}\left(\frac{x}{a}% \right),}}

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DLMF:14.15.E31

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{\displaystyle{\displaystyle-\infty<\zeta<\infty}}

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Defining formula

{\displaystyle{\displaystyle\operatorname{arcsinh}\NVar{z}}}

C4.S37.SS2.p1.m8adec

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Defining formula

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

C4.S37.SS2.p1.m10aadec

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Defining formula

{\displaystyle{\displaystyle x}}

C14.S1.XMD1.m1udec

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Defining formula

{\displaystyle{\displaystyle a}}

C14.S15.XMD13.m1fdec

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Defining formula

{\displaystyle{\displaystyle\zeta}}

C14.S15.XMD14.m1fdec

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Defining formula

{\displaystyle{\displaystyle\alpha}}

C14.S15.XMD9.m1mdec

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