DLMF:15.6.E9 (Q5047): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:15.6.E9	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathbf{F}\left(a,b;c;z\right)=\int_{0}^{1}\frac{t% ^{d-1}(1-t)^{c-d-1}}{(1-zt)^{a+b-\lambda}}\mathbf{F}\left({\lambda-a,\lambda-b% \atop d};zt\right)\mathbf{F}\left({a+b-\lambda,\lambda-d\atop c-d};\frac{(1-t)% z}{1-zt}\right)\mathrm{d}t,}}

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DLMF:15.6.E9

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{\displaystyle{\displaystyle|\operatorname{ph}\left(1-z\right)|<\pi}}

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{\displaystyle{\displaystyle\lambda\in\mathbb{C}}}

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{\displaystyle{\displaystyle\Re c>\Re d>0}}

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2ahdec

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Defining formula

{\displaystyle{\displaystyle\mathbb{C}}}

introduction.Sx4.p1.t1.r1.m2adec

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Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1ahdec

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Defining formula

{\displaystyle{\displaystyle\in}}

introduction.Sx4.p1.t1.r10.m2adec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3ahdec

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Defining formula

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

C1.S9.E7.m1ahdec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1aedec

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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.m2ahdec

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Defining formula

{\displaystyle{\displaystyle z}}

C15.S1.XMD3.m1hdec

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Defining formula

{\displaystyle{\displaystyle a}}

C15.S1.XMD4.m1hdec

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Defining formula

{\displaystyle{\displaystyle b}}

C15.S1.XMD5.m1hdec

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Sitelinks

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