DLMF:13.10.E15 (Q4474): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:13.10.E15	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}t^{\frac{1}{2}\nu}U\left(a,b,t% \right)J_{\nu}\left(2\sqrt{xt}\right)\mathrm{d}t=\frac{\Gamma\left(\nu-b+2% \right)}{\Gamma\left(a\right)}x^{\frac{1}{2}\nu}U\left(\nu-b+2,\nu-a+2,x\right% ),}}

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DLMF:13.10.E15

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{\displaystyle{\displaystyle\max\left(\Re b-2,-1\right)<\Re\nu<2\Re a+\tfrac{1% }{2}}}

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{\displaystyle{\displaystyle x>0}}

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{\displaystyle{\displaystyle\max\left(\Re b-2,-1\right)<\Re\nu<2\Re a+\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.m2abdec

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Defining formula

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

C5.S2.E1.m2ajdec

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Kummer confluent hypergeometric function

Defining formula

{\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}

C13.S2.E6.m2agdec

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Defining formula

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

C1.S4.SS4.m1andec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3andec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1aldec

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Defining formula

{\displaystyle{\displaystyle x}}

C13.S1.XMD4.m1cdec

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