DLMF:15.8.E22 (Q5079): Difference between revisions

From DRMF

Jump to navigation Jump to search

← Older edit Newer edit →

Revision as of 14:05, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:15.8.E22	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle F\left({a,b\atop\tfrac{1}{2}(a+b+1)};z\right)=% \left(\frac{\sqrt{1-z^{-1}}-1}{\sqrt{1-z^{-1}}+1}\right)^{a}F\left({a,\tfrac{1% }{2}(a+b)\atop a+b};\frac{4\sqrt{1-z^{-1}}}{\left(\sqrt{1-z^{-1}}+1\right)^{2}% }\right),}}

0 references

DLMF:15.8.E22

0 references

{\displaystyle{\displaystyle|\operatorname{ph}\left(-z\right)|<\pi}}

0 references

{\displaystyle{\displaystyle\Re z<\frac{1}{2}}}

0 references

$$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function

Defining formula

{\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}

C15.S2.E1.m2akdec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aldec

0 references

Defining formula

{\displaystyle{\displaystyle\operatorname{ph}}}

C1.S9.E7.m1aldec

0 references

Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1aedec

0 references

Defining formula

{\displaystyle{\displaystyle z}}

C15.S1.XMD3.m1udec

0 references

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5079&oldid=43356"