Formula:5553

Digital Library of Mathematical Functions ID 14.15.E10

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

Symbols List

• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\alpha}}$: α
• ${\displaystyle{\displaystyle\eta}}$: η
 

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