DLMF:14.23.E3 (Q4949)

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Language	Label	Description	Also known as
English	DLMF:14.23.E3	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\boldsymbol{Q}^{\mu}_{\nu}\left(x\pm i0\right)=% \frac{e^{\mp\nu\pi i/2}\pi^{3/2}\left(1-x^{2}\right)^{\mu/2}}{2^{\nu+1}}\left(% \frac{x\mathbf{F}\left(\frac{1}{2}\mu-\frac{1}{2}\nu+\frac{1}{2},\frac{1}{2}% \nu+\frac{1}{2}\mu+1;\frac{3}{2};x^{2}\right)}{\Gamma\left(\frac{1}{2}\nu-% \frac{1}{2}\mu+\frac{1}{2}\right)\Gamma\left(\frac{1}{2}\nu+\frac{1}{2}\mu+% \frac{1}{2}\right)}\mp i\frac{\mathbf{F}\left(\frac{1}{2}\mu-\frac{1}{2}\nu,% \frac{1}{2}\nu+\frac{1}{2}\mu+\frac{1}{2};\frac{1}{2};x^{2}\right)}{\Gamma% \left(\frac{1}{2}\nu-\frac{1}{2}\mu+1\right)\Gamma\left(\frac{1}{2}\nu+\frac{1% }{2}\mu+1\right)}\right).}}

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DLMF:14.23.E3

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Defining formula

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

C5.S2.E1.m2aadec

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Defining formula

{\displaystyle{\displaystyle\boldsymbol{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(% \NVar{z}\right)}}

C14.S21.SS1.p1.m3aadec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2abdec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2abdec

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Defining formula

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

C1.S9.E1.m2abdec

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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.m2adec

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Defining formula

{\displaystyle{\displaystyle x}}

C14.S1.XMD1.m1bdec

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Defining formula

{\displaystyle{\displaystyle\mu}}

C14.S1.XMD7.m1bdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C14.S1.XMD8.m1bdec

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