DLMF:10.22.E19 (Q3393)

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Language	Label	Description	Also known as
English	DLMF:10.22.E19	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\frac{1}{2}\pi}J_{\mu}\left(z\sin\theta% \right)(\sin\theta)^{\mu+1}(\cos\theta)^{2\nu+1}\mathrm{d}\theta=2^{\nu}\Gamma% \left(\nu+1\right)z^{-\nu-1}J_{\mu+\nu+1}\left(z\right),}}

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DLMF:10.22.E19

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{\displaystyle{\displaystyle\Re\mu>-1}}

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{\displaystyle{\displaystyle\Re\nu>-1}}

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Bessel function of the first kind

Defining formula

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

C10.S2.E2.m2akdec

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Defining formula

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

C5.S2.E1.m2abdec

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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.m2aedec

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Defining formula

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

C1.S4.SS4.m1ardec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3ardec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1afdec

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Defining formula

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

C4.S14.E1.m2addec

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Defining formula

{\displaystyle{\displaystyle z}}

C10.S1.XMD6.m1mdec

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Sitelinks

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