DLMF:14.15.E10 (Q4856)

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Language	Label	Description	Also known as
English	DLMF:14.15.E10	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\alpha\ln\left(\left(\alpha^{2}+\eta^{2}\right)^{1% /2}+\alpha\right)-\alpha\ln\eta-\left(\alpha^{2}+\eta^{2}\right)^{1/2}=\frac{1% }{2}\ln\left(\frac{\left(1+\alpha^{2}\right)x^{2}+1-\alpha^{2}-2x\left(\alpha^% {2}x^{2}-\alpha^{2}+1\right)^{1/2}}{\left(x^{2}-1\right)\left(1-\alpha^{2}% \right)}\right)+\frac{1}{2}\alpha\ln\left(\frac{\alpha^{2}\left(2x^{2}-1\right% )+1+2\alpha x\left(\alpha^{2}x^{2}-\alpha^{2}+1\right)^{1/2}}{1-\alpha^{2}}% \right).}}

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DLMF:14.15.E10

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principal branch of logarithm function

Defining formula

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

C4.S2.E2.m2aadec

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Defining formula

{\displaystyle{\displaystyle x}}

C14.S1.XMD1.m1gdec

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Defining formula

{\displaystyle{\displaystyle\alpha}}

C14.S15.XMD3.m1fdec

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