DLMF:10.22.E70 (Q3444)

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Language	Label	Description	Also known as
English	DLMF:10.22.E70	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}Y_{\nu}\left(at\right)J_{\nu+1}% \left(bt\right)\frac{t\mathrm{d}t}{t^{2}-z^{2}}=\frac{1}{2}\pi J_{\nu+1}\left(% bz\right){H^{(1)}_{\nu}}\left(az\right),}}

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DLMF:10.22.E70

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{\displaystyle{\displaystyle\Re\nu>-\tfrac{3}{2},\Im z>0}}

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{\displaystyle{\displaystyle a\geq b>0}}

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{\displaystyle{\displaystyle\Re\nu>-\tfrac{3}{2},\Im z>0}}

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Bessel function of the first kind

Defining formula

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

C10.S2.E2.m2abcdec

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Bessel function of the second kind

Defining formula

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

C10.S2.E3.m2akdec

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Bessel function of the third kind (or Hankel function)

Defining formula

{\displaystyle{\displaystyle{H^{(1)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}

C10.S2.E5.m2aadec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aabdec

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Sitelinks

Wikipedia(0 entries)

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