DLMF:15.9.E20 (Q5110): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:15.9.E20	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathbf{F}\left({a,b\atop\tfrac{1}{2}(a+b+1)};z% \right)=\left(-z(1-z)\right)^{\ifrac{(1-a-b)}{4}}\*P^{\ifrac{(1-a-b)}{2}}_{% \ifrac{(a-b-1)}{2}}\left(1-2z\right),}}

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DLMF:15.9.E20

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

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Defining formula

{\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}

C14.S21.SS1.p1.m1addec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aedec

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Defining formula

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

C1.S9.E7.m1addec

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$$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Olver’s hypergeometric function

Defining formula

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

C15.S2.E2.m2addec

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Defining formula

{\displaystyle{\displaystyle z}}

C15.S1.XMD3.m1edec

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Defining formula

{\displaystyle{\displaystyle a}}

C15.S1.XMD4.m1ddec

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Defining formula

{\displaystyle{\displaystyle b}}

C15.S1.XMD5.m1cdec

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