DLMF:18.17.E31 (Q5772)

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Language	Label	Description	Also known as
English	DLMF:18.17.E31	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}e^{-ax}x^{\nu-2n}L^{(\nu-2n)}_{2n% -1}\left(ax\right)\cos\left(xy\right)\mathrm{d}x=i\frac{(-1)^{n}\Gamma\left(% \nu\right)}{2(2n-1)!}y^{2n-1}\left((a+iy)^{-\nu}-(a-iy)^{-\nu}\right),}}

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DLMF:18.17.E31

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{\displaystyle{\displaystyle a>0}}

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Defining formula

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

C5.S2.E1.m2ajdec

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Defining formula

{\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}% \right)}}

C18.S3.T1.t1.r12.m2afdec

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cosine function

Defining formula

{\displaystyle{\displaystyle\cos\NVar{z}}}

C4.S14.E2.m2aidec

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Defining formula

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

C1.S4.SS4.m1aaddec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2andec

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Defining formula

{\displaystyle{\displaystyle!}}

introduction.Sx4.p1.t1.r15.m5agdec

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Defining formula

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

C1.S9.E1.m2acdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aaddec

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Defining formula

{\displaystyle{\displaystyle y}}

C18.S1.XMD1.m1zdec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1addec

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Defining formula

{\displaystyle{\displaystyle x}}

C18.S2.XMD3.m1abdec

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Sitelinks

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