DLMF:15.12.E9 (Q5169)

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Language	Label	Description	Also known as
English	DLMF:15.12.E9	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle(z+1)^{3\lambda/2}(2\lambda)^{c-1}\mathbf{F}\left(% {a+\lambda,b+2\lambda\atop c};-z\right)={\lambda^{-1/3}\left(e^{\pi\mathrm{i}(% a-c+\lambda+(1/3))}\mathrm{Ai}\left(e^{-\ifrac{2\pi\mathrm{i}}{3}}\lambda^{% \ifrac{2}{3}}\beta^{2}\right)+e^{\pi\mathrm{i}(c-a-\lambda-(1/3))}\mathrm{Ai}% \left(e^{\ifrac{2\pi\mathrm{i}}{3}}\lambda^{\ifrac{2}{3}}\beta^{2}\right)% \right)\left(a_{0}(\zeta)+O(\lambda^{-1})\right)}+\lambda^{-2/3}\left(e^{\pi% \mathrm{i}(a-c+\lambda+(2/3))}\mathrm{Ai}'\left(e^{-\ifrac{2\pi\mathrm{i}}{3}}% \lambda^{\ifrac{2}{3}}\beta^{2}\right)+e^{\pi\mathrm{i}(c-a-\lambda-(2/3))}% \mathrm{Ai}'\left(e^{\ifrac{2\pi\mathrm{i}}{3}}\lambda^{\ifrac{2}{3}}\beta^{2}% \right)\right)\left(a_{1}(\zeta)+O(\lambda^{-1})\right),}}

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DLMF:15.12.E9

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Defining formula

{\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}

C9.S2.SS1.m1adec

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order not exceeding

Defining formula

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

C2.S1.E3.m2acdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aadec

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base of natural logarithm

Defining formula

{\displaystyle{\displaystyle\mathrm{e}}}

C4.S2.E11.m2aadec

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Defining formula

{\displaystyle{\displaystyle\mathrm{i}}}

C1.S9.E1.m2adec

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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.m2aadec

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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.m1edec

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Defining formula

{\displaystyle{\displaystyle b}}

C15.S1.XMD5.m1edec

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Defining formula

{\displaystyle{\displaystyle c}}

C15.S1.XMD6.m1edec

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Defining formula

{\displaystyle{\displaystyle\zeta}}

C15.S12.XMD5.m1bdec

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Defining formula

{\displaystyle{\displaystyle\beta}}

C15.S12.XMD6.m1dec

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Defining formula

{\displaystyle{\displaystyle a_{j}(\zeta)}}

C15.S12.XMD7.m1dec

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