DLMF:15.10.E12 (Q5128)

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Language	Label	Description	Also known as
English	DLMF:15.10.E12	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle w_{2}(z)={z^{1-c}}F\left({a-c+1,b-c+1\atop 2-c};z% \right)={z^{1-c}(1-z)^{c-a-b}}\*F\left({1-a,1-b\atop 2-c};z\right)={z^{1-c}(1-% z)^{c-a-1}}\*F\left({a-c+1,1-b\atop 2-c};\frac{z}{z-1}\right)={z^{1-c}(1-z)^{c% -b-1}}\*F\left({1-a,b-c+1\atop 2-c};\frac{z}{z-1}\right).}}

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DLMF:15.10.E12

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

Defining formula

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

C15.S2.E1.m2agdec

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Defining formula

{\displaystyle{\displaystyle z}}

C15.S1.XMD3.m1kdec

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Defining formula

{\displaystyle{\displaystyle a}}

C15.S1.XMD4.m1kdec

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Defining formula

{\displaystyle{\displaystyle b}}

C15.S1.XMD5.m1kdec

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Defining formula

{\displaystyle{\displaystyle c}}

C15.S1.XMD6.m1hdec

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Defining formula

{\displaystyle{\displaystyle w_{m}(z)}}

C15.S10.XMD2.m1adec

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