DLMF:11.10.E31 (Q4053)

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Language	Label	Description	Also known as
English	DLMF:11.10.E31	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{\mathbf{E}_{\nu}\left(z\right)=}\\ {-2\cos\left(\tfrac{1}{2}\nu\pi\right)\sum_{k=0}^{\infty}(-1)^{k}J_{k-\frac{1}% {2}\nu+\frac{1}{2}}\left(\tfrac{1}{2}z\right)J_{k+\frac{1}{2}\nu+\frac{1}{2}}% \left(\tfrac{1}{2}z\right)}+{2\sin\left(\tfrac{1}{2}\nu\pi\right)\sideset{}{{}% ^{\prime}}{\sum}_{k=0}^{\infty}(-1)^{k}J_{k-\frac{1}{2}\nu}\left(\tfrac{1}{2}z% \right)J_{k+\frac{1}{2}\nu}\left(\tfrac{1}{2}z\right)},}}

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DLMF:11.10.E31

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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\mathbf{E}_{\NVar{\nu}}\left(\NVar{z}\right)}}

C11.S10.E2.m2ardec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2axdec

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cosine function

Defining formula

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

C4.S14.E2.m2amdec

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Defining formula

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

C4.S14.E1.m2andec

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Defining formula

{\displaystyle{\displaystyle z}}

C11.S1.XMD2.m1abdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C11.S1.XMD3.m1zdec

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Defining formula

{\displaystyle{\displaystyle k}}

C11.S1.XMD5.m1edec

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Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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