DLMF:15.5.E13 (Q5030)

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Language	Label	Description	Also known as
English	DLMF:15.5.E13	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle(c-a-b)F\left(a,b;c;z\right)+a(1-z)F\left(a+1,b;c;% z\right)-(c-b)F\left(a,b-1;c;z\right)=0,}}

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DLMF:15.5.E13

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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.m2akdec

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Defining formula

{\displaystyle{\displaystyle z}}

C15.S1.XMD3.m1ldec

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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.m1kdec

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