DLMF:11.5.E9 (Q3976)

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Language	Label	Description	Also known as
English	DLMF:11.5.E9	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle(\tfrac{1}{2}z)^{-\nu-1}\mathbf{L}_{\nu}\left(z% \right)=\frac{1}{2\pi i}\int_{\infty}^{(0+)}\frac{\pi\csc\left(\pi s\right)}{% \Gamma\left(\tfrac{3}{2}+s\right)\Gamma\left(\tfrac{3}{2}+\nu+s\right)}(-% \tfrac{1}{4}z^{2})^{s}\mathrm{d}s.}}

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DLMF:11.5.E9

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Defining formula

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

C5.S2.E1.m2afdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2ahdec

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cosecant function

Defining formula

{\displaystyle{\displaystyle\csc\NVar{z}}}

C4.S14.E5.m2aadec

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Defining formula

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

C1.S4.SS4.m1ahdec

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Defining formula

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

C1.S9.E1.m2aadec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3ahdec

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modified Struve function

Defining formula

{\displaystyle{\displaystyle\mathbf{L}_{\NVar{\nu}}\left(\NVar{z}\right)}}

C11.S2.E2.m2abdec

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Defining formula

{\displaystyle{\displaystyle z}}

C11.S1.XMD2.m1fdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C11.S1.XMD3.m1fdec

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