DLMF:10.22.E43 (Q3417)

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Language	Label	Description	Also known as
English	DLMF:10.22.E43	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}t^{\mu}J_{\nu}\left(t\right)% \mathrm{d}t=2^{\mu}\frac{\Gamma\left(\tfrac{1}{2}\nu+\tfrac{1}{2}\mu+\tfrac{1}% {2}\right)}{\Gamma\left(\tfrac{1}{2}\nu-\tfrac{1}{2}\mu+\tfrac{1}{2}\right)},}}

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DLMF:10.22.E43

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{\displaystyle{\displaystyle\Re(\mu+\nu)>-1}}

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{\displaystyle{\displaystyle\Re\mu<\tfrac{1}{2}}}

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Bessel function of the first kind

Defining formula

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

C10.S2.E2.m2aagdec

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Defining formula

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

C5.S2.E1.m2aidec

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Defining formula

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

C1.S4.SS4.m1aapdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aapdec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1axdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C10.S1.XMD7.m1acdec

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