DLMF:15.9.E18 (Q5108)

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Language	Label	Description	Also known as
English	DLMF:15.9.E18	No description defined

Statements

Defining formula

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

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DLMF:15.9.E18

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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.m1abdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2acdec

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Defining formula

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

C1.S9.E7.m1abdec

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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.m2abdec

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Defining formula

{\displaystyle{\displaystyle z}}

C15.S1.XMD3.m1cdec

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Defining formula

{\displaystyle{\displaystyle a}}

C15.S1.XMD4.m1bdec

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Defining formula

{\displaystyle{\displaystyle b}}

C15.S1.XMD5.m1adec

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