DLMF:15.12.E7 (Q5167): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:15.12.E7	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle F\left({a,b-\lambda\atop c+\lambda};-z\right)=2^{% b-c+(1/2)}\left(\frac{z+1}{2\sqrt{z}}\right)^{\lambda}\left(\lambda^{a/2}U% \left(a-\tfrac{1}{2},-\alpha\sqrt{\lambda}\right)\left((1+z)^{c-a-b}z^{1-c}% \left(\frac{\alpha}{z-1}\right)^{1-a}+O(\lambda^{-1})\right)+\frac{\lambda^{% \ifrac{(a-1)}{2}}}{\alpha}U\left(a-\tfrac{3}{2},-\alpha\sqrt{\lambda}\right)% \left((1+z)^{c-a-b}z^{1-c}\left(\frac{\alpha}{z-1}\right)^{1-a}-2^{c-b-(\ifrac% {1}{2})}\left(\frac{\alpha}{z-1}\right)^{a}+O(\lambda^{-1})\right)\right),}}

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DLMF:15.12.E7

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order not exceeding

Defining formula

{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

C2.S1.E3.m2abdec

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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.m2abdec

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Defining formula

{\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}

C12.S2.SS1.p1.m1adec

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Defining formula

{\displaystyle{\displaystyle z}}

C15.S1.XMD3.m1fdec

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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.m1ddec

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Defining formula

{\displaystyle{\displaystyle c}}

C15.S1.XMD6.m1ddec

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Defining formula

{\displaystyle{\displaystyle\alpha}}

C15.S12.XMD4.m1dec

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