DLMF:18.17.E30 (Q5771)

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Language	Label	Description	Also known as
English	DLMF:18.17.E30	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}x^{2n}e^{-\frac{1}{2}x^{2}}L^{(n-% \frac{1}{2})}_{n}\left(\tfrac{1}{2}x^{2}\right)\cos\left(xy\right)\mathrm{d}x=% \sqrt{\tfrac{1}{2}\pi}y^{2n}e^{-\frac{1}{2}y^{2}}L^{(n-\frac{1}{2})}_{n}\left(% \tfrac{1}{2}y^{2}\right).}}

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DLMF:18.17.E30

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Defining formula

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

C18.S3.T1.t1.r12.m2aedec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aqdec

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cosine function

Defining formula

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

C4.S14.E2.m2ahdec

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Defining formula

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

C1.S4.SS4.m1aacdec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2amdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aacdec

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Defining formula

{\displaystyle{\displaystyle y}}

C18.S1.XMD1.m1ydec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1acdec

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Defining formula

{\displaystyle{\displaystyle x}}

C18.S2.XMD3.m1aadec

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