DLMF:8.18.E9 (Q2677)

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Language	Label	Description	Also known as
English	DLMF:8.18.E9	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle I_{x}\left(a,b\right)\sim\tfrac{1}{2}% \operatorname{erfc}\left(-\eta\sqrt{b/2}\right)+\frac{1}{\sqrt{2\pi(a+b)}}\*% \left(\frac{x}{x_{0}}\right)^{a}\left(\frac{1-x}{1-x_{0}}\right)^{b}\sum_{k=0}% ^{\infty}\frac{(-1)^{k}c_{k}(\eta)}{(a+b)^{k}},}}

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DLMF:8.18.E9

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incomplete beta function

Defining formula

{\displaystyle{\displaystyle I_{\NVar{x}}\left(\NVar{a},\NVar{b}\right)}}

C8.S17.E2.m2abdec

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Defining formula

{\displaystyle{\displaystyle\sim}}

C2.S1.SS3.p1.m11aadec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2adec

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complementary error function

Defining formula

{\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}

C7.S2.E2.m2adec

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Defining formula

{\displaystyle{\displaystyle k}}

C8.S1.XMD5.m1ddec

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Defining formula

{\displaystyle{\displaystyle a}}

C8.S17.XMD1.m1edec

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Defining formula

{\displaystyle{\displaystyle b}}

C8.S17.XMD2.m1gdec

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Defining formula

{\displaystyle{\displaystyle x}}

C8.S17.XMD3.m1edec

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Defining formula

{\displaystyle{\displaystyle c_{k}(\eta)}}

C8.S18.XMD4.m1dec

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