DLMF:10.9.E30 (Q3100)

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Language	Label	Description	Also known as
English	DLMF:10.9.E30	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{J_{\nu}^{2}}\left(z\right)+{Y_{\nu}^{2}}\left(z% \right)=\frac{8}{\pi^{2}}\int_{0}^{\infty}\cosh\left(2\nu t\right)K_{0}\left(2% z\sinh t\right)\mathrm{d}t,}}

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DLMF:10.9.E30

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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.m2aqdec

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Bessel function of the second kind

Defining formula

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

C10.S2.E3.m2agdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aacdec

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Defining formula

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

C1.S4.SS4.m1aacdec

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hyperbolic cosine function

Defining formula

{\displaystyle{\displaystyle\cosh\NVar{z}}}

C4.S28.E2.m2ahdec

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hyperbolic sine function

Defining formula

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

C4.S28.E1.m2ahdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aacdec

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modified Bessel function of the second kind

Defining formula

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

C10.S25.E3.m2adec

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Defining formula

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

C1.S9.E7.m1ahdec

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Defining formula

{\displaystyle{\displaystyle z}}

C10.S1.XMD6.m1xdec

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Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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