DLMF:18.17.E29 (Q5770)

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Language	Label	Description	Also known as
English	DLMF:18.17.E29	No description defined

Statements

Defining formula

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

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DLMF:18.17.E29

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Defining formula

{\displaystyle{\displaystyle\mathit{He}_{\NVar{n}}\left(\NVar{x}\right)}}

C18.S3.T1.t1.r14.m2agdec

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Defining formula

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

C18.S3.T1.t1.r12.m2addec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2apdec

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cosine function

Defining formula

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

C4.S14.E2.m2agdec

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Defining formula

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

C1.S4.SS4.m1aabdec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2aldec

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Defining formula

{\displaystyle{\displaystyle!}}

introduction.Sx4.p1.t1.r15.m5afdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aabdec

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Defining formula

{\displaystyle{\displaystyle y}}

C18.S1.XMD1.m1xdec

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Defining formula

{\displaystyle{\displaystyle m}}

C18.S1.XMD5.m1cdec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1abdec

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Defining formula

{\displaystyle{\displaystyle x}}

C18.S2.XMD3.m1zdec

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Sitelinks

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DRMF related sites(0 entries)

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