DLMF:18.17.E21 (Q5762)

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Language	Label	Description	Also known as
English	DLMF:18.17.E21	No description defined

Statements

Defining formula

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

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DLMF:18.17.E21

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Bessel function of the first kind

Defining formula

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

C10.S2.E2.m2addec

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Defining formula

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

C18.S3.T1.t1.r10.m2addec

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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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Defining formula

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

C1.S4.SS4.m1atdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3atdec

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Defining formula

{\displaystyle{\displaystyle\sin\NVar{z}}}

C4.S14.E1.m2acdec

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Defining formula

{\displaystyle{\displaystyle y}}

C18.S1.XMD1.m1pdec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1tdec

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Sitelinks

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