DLMF:10.9.E28 (Q3098)

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Language	Label	Description	Also known as
English	DLMF:10.9.E28	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle J_{\nu}\left(z\right)J_{\nu}\left(\zeta\right)=% \frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\*\exp\left(\frac{1}{2}t-\frac{z^{% 2}+\zeta^{2}}{2t}\right)I_{\nu}\left(\frac{z\zeta}{t}\right)\frac{\mathrm{d}t}% {t},}}

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DLMF:10.9.E28

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{\displaystyle{\displaystyle\Re\nu>-1}}

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Bessel function of the first kind

Defining formula

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

C10.S2.E2.m2aodec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aaadec

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Defining formula

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

C1.S4.SS4.m1aaadec

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exponential function

Defining formula

{\displaystyle{\displaystyle\exp\NVar{z}}}

C4.S2.E19.m2aadec

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Defining formula

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

C1.S9.E1.m2andec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aaadec

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modified Bessel function of the first kind

Defining formula

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

C10.S25.E2.m2adec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1aidec

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Defining formula

{\displaystyle{\displaystyle z}}

C10.S1.XMD6.m1wdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C10.S1.XMD7.m1wdec

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Defining formula

{\displaystyle{\displaystyle c}}

C10.S9.XMD2.m1dec

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