DLMF:13.20.E9 (Q4598)

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Language	Label	Description	Also known as
English	DLMF:13.20.E9	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\zeta\sqrt{\zeta^{2}+\alpha^{2}}+\alpha^{2}% \operatorname{arcsinh}\left(\frac{\zeta}{\alpha}\right)=\frac{X}{\mu}-\frac{2% \kappa}{\mu}\ln\left(\frac{X+x-2\kappa}{2\sqrt{\mu^{2}-\kappa^{2}}}\right)-2% \ln\left(\frac{\mu X+2\mu^{2}-\kappa x}{x\sqrt{\mu^{2}-\kappa^{2}}}\right).}}

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DLMF:13.20.E9

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Defining formula

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

C4.S37.SS2.p1.m8adec

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principal branch of logarithm function

Defining formula

{\displaystyle{\displaystyle\ln\NVar{z}}}

C4.S2.E2.m2adec

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Defining formula

{\displaystyle{\displaystyle x}}

C13.S1.XMD4.m1fdec

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Defining formula

{\displaystyle{\displaystyle\alpha}}

C13.S20.XMD2.m1adec

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Defining formula

{\displaystyle{\displaystyle X}}

C13.S20.XMD3.m1adec

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Defining formula

{\displaystyle{\displaystyle X}}

C13.S20.XMD3.m1adec

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