DLMF:10.9.E22 (Q3092)

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Language	Label	Description	Also known as
English	DLMF:10.9.E22	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle J_{\nu}\left(x\right)=\frac{1}{2\pi i}\int_{-i% \infty}^{i\infty}\frac{\Gamma\left(-t\right)(\tfrac{1}{2}x)^{\nu+2t}}{\Gamma% \left(\nu+t+1\right)}\mathrm{d}t,}}

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DLMF:10.9.E22

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{\displaystyle{\displaystyle\Re\nu>0}}

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{\displaystyle{\displaystyle\Re\nu>0}}

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{\displaystyle{\displaystyle x>0}}

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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.m2aedec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2audec

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Defining formula

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

C1.S4.SS4.m1audec

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Defining formula

{\displaystyle{\displaystyle\mathrm{i}}}

C1.S9.E1.m2ajdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3audec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1afdec

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Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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