DLMF:18.12.E6 (Q5648)

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Language	Label	Description	Also known as
English	DLMF:18.12.E6	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\Gamma\left(\lambda+\tfrac{1}{2}\right)e^{z\cos% \theta}(\tfrac{1}{2}z\sin\theta)^{\frac{1}{2}-\lambda}J_{\lambda-\frac{1}{2}}% \left(z\sin\theta\right)=\sum_{n=0}^{\infty}\frac{C^{(\lambda)}_{n}\left(\cos% \theta\right)}{{\left(2\lambda\right)_{n}}}z^{n},}}

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DLMF:18.12.E6

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{\displaystyle{\displaystyle 0\leq\theta\leq\pi}}

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Bessel function of the first kind

Defining formula

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

C10.S2.E2.m2aadec

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Defining formula

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

C5.S2.E1.m2aadec

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Defining formula

{\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

C5.S2.SS3.m1abdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2adec

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cosine function

Defining formula

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

C4.S14.E2.m2adec

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base of natural logarithm

Defining formula

{\displaystyle{\displaystyle\mathrm{e}}}

C4.S2.E11.m2adec

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Defining formula

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

C4.S14.E1.m2adec

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Defining formula

{\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}% \right)}}

C18.S3.T1.t1.r3.m2abdec

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Defining formula

{\displaystyle{\displaystyle z}}

C18.S1.XMD2.m1edec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1edec

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Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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