DLMF:14.15.E22 (Q4868)

From DRMF

Jump to navigation Jump to search

No description defined

Language	Label	Description	Also known as
English	DLMF:14.15.E22	No description defined

Statements

Defining formula

{\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)},}}

0 references

DLMF:14.15.E22

0 references

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

0 references

principal branch of logarithm function

Defining formula

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

C4.S2.E2.m2abdec

0 references

Defining formula

{\displaystyle{\displaystyle x}}

C14.S1.XMD1.m1mdec

0 references

Defining formula

{\displaystyle{\displaystyle y}}

C14.S15.XMD11.m1edec

0 references

Defining formula

{\displaystyle{\displaystyle\alpha}}

C14.S15.XMD9.m1fdec

0 references

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4868&oldid=35360"