DLMF:9.10.E16 (Q2899)

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Language	Label	Description	Also known as
English	DLMF:9.10.E16	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}e^{-pt}\mathrm{Bi}\left(-t\right)% \mathrm{d}t={\frac{1}{\sqrt{3}}e^{p^{3}/3}\left(\frac{\Gamma\left(\tfrac{2}{3}% ,\tfrac{1}{3}p^{3}\right)}{\Gamma\left(\tfrac{2}{3}\right)}-\frac{\Gamma\left(% \tfrac{1}{3},\tfrac{1}{3}p^{3}\right)}{\Gamma\left(\tfrac{1}{3}\right)}\right)% },}}

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DLMF:9.10.E16

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{\displaystyle{\displaystyle\Re p>0}}

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Defining formula

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

C9.S2.SS1.m2addec

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Defining formula

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

C5.S2.E1.m2abdec

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Defining formula

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

C1.S4.SS4.m1aodec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2acdec

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incomplete gamma function

Defining formula

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

C8.S2.E2.m2aadec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aodec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1abdec

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Defining formula

{\displaystyle{\displaystyle p}}

C9.S10.XMD2.m1cdec

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