Formula:5565

Digital Library of Mathematical Functions ID 14.15.E22

${\displaystyle{\displaystyle{\left(\alpha^{2}-y\right)^{1/2}+\tfrac{1}{2}\alpha\ln|y|-\alpha\ln\left(\left(\alpha^{2}-y\right)^{1/2}+\alpha\right)}={\ln\left(\frac{x+\left(x^{2}-1+\alpha^{2}\right)^{1/2}}{\left(1-\alpha^{2}\right)^{1/2}}\right)+\frac{\alpha}{2}\ln\left(\frac{\left(1-\alpha^{2}\right)\left|1-x^{2}\right|}{\left(1+\alpha^{2}\right)x^{2}-1+\alpha^{2}+2\alpha x\left(x^{2}-1+\alpha^{2}\right)^{1/2}}\right)},}}$

Constraint(s)

${\displaystyle{\displaystyle y\leq\alpha^{2}}}$

Symbols List

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

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