DLMF:14.20.E21 (Q4942)

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Language	Label	Description	Also known as
English	DLMF:14.20.E21	No description defined

Statements

Defining formula

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

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DLMF:14.20.E21

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Defining formula

{\displaystyle{\displaystyle\operatorname{arccos}\NVar{z}}}

C4.S23.SS2.p1.m6adec

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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}}

C14.S1.XMD1.m1vdec

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Defining formula

{\displaystyle{\displaystyle\alpha}}

C14.S20.XMD5.m1ddec

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