DLMF:10.9.E6 (Q3071)

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Language	Label	Description	Also known as
English	DLMF:10.9.E6	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle J_{\nu}\left(z\right)=\frac{1}{\pi}\int_{0}^{\pi}% \cos\left(z\sin\theta-\nu\theta\right)\mathrm{d}\theta-\frac{\sin\left(\nu\pi% \right)}{\pi}\int_{0}^{\infty}e^{-z\sinh t-\nu t}\mathrm{d}t,}}

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DLMF:10.9.E6

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{\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{2}\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.m2acdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aedec

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cosine function

Defining formula

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

C4.S14.E2.m2addec

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Defining formula

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

C1.S4.SS4.m1aedec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2abdec

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hyperbolic sine function

Defining formula

{\displaystyle{\displaystyle\sinh\NVar{z}}}

C4.S28.E1.m2adec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aedec

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Defining formula

{\displaystyle{\displaystyle\operatorname{ph}}}

C1.S9.E7.m1aadec

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Defining formula

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

C4.S14.E1.m2aedec

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Defining formula

{\displaystyle{\displaystyle z}}

C10.S1.XMD6.m1edec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C10.S1.XMD7.m1bdec

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Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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