DLMF:10.43.E26 (Q3640): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:10.43.E26	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}\frac{K_{\mu}\left(at\right)J_{% \nu}\left(bt\right)}{t^{\lambda}}\mathrm{d}t=\frac{b^{\nu}\Gamma\left(\frac{1}% {2}\nu-\frac{1}{2}\lambda+\frac{1}{2}\mu+\frac{1}{2}\right)\Gamma\left(\frac{1% }{2}\nu-\frac{1}{2}\lambda-\frac{1}{2}\mu+\frac{1}{2}\right)}{2^{\lambda+1}a^{% \nu-\lambda+1}}\*\mathbf{F}\left(\frac{\nu-\lambda+\mu+1}{2},\frac{\nu-\lambda% -\mu+1}{2};\nu+1;-\frac{b^{2}}{a^{2}}\right),}}

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DLMF:10.43.E26

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{\displaystyle{\displaystyle\Re(\nu+1-\lambda)>|\Re\mu|,\Re a>|\Im b|}}

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Bessel function of the first kind

Defining formula

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

C10.S2.E2.m2adec

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Defining formula

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

C5.S2.E1.m2agdec

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Defining formula

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

C1.S4.SS4.m1audec

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Defining formula

{\displaystyle{\displaystyle\Im}}

C1.S9.E2.m2abdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3audec

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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.m2aldec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1aidec

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$$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Olver’s hypergeometric function

Defining formula

{\displaystyle{\displaystyle\mathbf{F}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z% }\right)}}

C15.S2.E2.m2adec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C10.S1.XMD7.m1mdec

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Sitelinks

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