DLMF:9.5.E8 (Q2780)

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Language	Label	Description	Also known as
English	DLMF:9.5.E8	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathrm{Ai}\left(z\right)=\frac{e^{-\zeta}\zeta^{% \ifrac{-1}{6}}}{\sqrt{\pi}(48)^{\ifrac{1}{6}}\Gamma\left(\frac{5}{6}\right)}% \int_{0}^{\infty}e^{-t}t^{-\ifrac{1}{6}}\left(2+\frac{t}{\zeta}\right)^{-% \ifrac{1}{6}}\mathrm{d}t,}}

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DLMF:9.5.E8

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{\displaystyle{\displaystyle|\operatorname{ph}z|<\frac{2}{3}\pi}}

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Defining formula

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

C9.S2.SS1.m1aedec

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Defining formula

{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

C5.S2.E1.m2adec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2agdec

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Defining formula

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

C1.S4.SS4.m1agdec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2addec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3agdec

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Defining formula

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

C1.S9.E7.m1abdec

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Defining formula

{\displaystyle{\displaystyle z}}

C9.S1.XMD3.m1ddec

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Defining formula

{\displaystyle{\displaystyle\zeta}}

C9.S5.XMD1.m1adec

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