DLMF:18.17.E20 (Q5761): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:18.17.E20	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{1}P_{n}\left(1-2x^{2}\right)\cos\left(xy% \right)\mathrm{d}x=(-1)^{n}\tfrac{1}{2}\pi J_{n+\frac{1}{2}}\left(\tfrac{1}{2}% y\right)J_{-n-\frac{1}{2}}\left(\tfrac{1}{2}y\right),}}

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DLMF:18.17.E20

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Bessel function of the first kind

Defining formula

{\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}

C10.S2.E2.m2acdec

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Defining formula

{\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}

C18.S3.T1.t1.r10.m2acdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2agdec

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cosine function

Defining formula

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

C4.S14.E2.m2acdec

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Defining formula

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

C1.S4.SS4.m1asdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3asdec

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Defining formula

{\displaystyle{\displaystyle y}}

C18.S1.XMD1.m1odec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1sdec

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Sitelinks

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