DLMF:5.18.E12 (Q2199)

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Language	Label	Description	Also known as
English	DLMF:5.18.E12	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathrm{B}_{q}\left(a,b\right)=\int_{0}^{1}\frac{t% ^{a-1}\left(tq;q\right)_{\infty}}{\left(tq^{b};q\right)_{\infty}}{\mathrm{d}}_% {q}t,}}

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DLMF:5.18.E12

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{\displaystyle{\displaystyle\Re a>0}}

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{\displaystyle{\displaystyle\Re b>0}}

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{\displaystyle{\displaystyle 0<q<1}}

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{\displaystyle{\displaystyle\Re a>0}}

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{\displaystyle{\displaystyle\Re b>0}}

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3adec

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$$q$$ -beta function

Defining formula

{\displaystyle{\displaystyle\mathrm{B}_{\NVar{q}}\left(\NVar{a},\NVar{b}\right% )}}

C5.S18.E11.m2aadec

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Defining formula

{\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}

C17.S2.SS1.p1.m2addec

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Defining formula

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

C17.S2.SS5.p1.m3adec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1adec

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Defining formula

{\displaystyle{\displaystyle q}}

C5.S1.XMD10.m1kdec

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Defining formula

{\displaystyle{\displaystyle a}}

C5.S1.XMD8.m1cdec

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Defining formula

{\displaystyle{\displaystyle b}}

C5.S1.XMD9.m1adec

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