DLMF:10.22.E64 (Q3438): Difference between revisions

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English	DLMF:10.22.E64	No description defined

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Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}J_{\mu+2n+1}\left(at\right)J_{\mu% }\left(bt\right)\mathrm{d}t=\begin{cases}\dfrac{b^{\mu}\Gamma\left(\mu+n+1% \right)}{a^{\mu+1}n!}\mathbf{F}\left(-n,\mu+n+1;\mu+1;\dfrac{b^{2}}{a^{2}}% \right),&0<b<a,\\ (-1)^{n}/(2a),&b=a(>0),\\ 0,&0<a<b.\end{cases}}}

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DLMF:10.22.E64

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Bessel function of the first kind

Defining formula

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

C10.S2.E2.m2aawdec

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Defining formula

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

C5.S2.E1.m2audec

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Defining formula

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

C1.S4.SS4.m1abkdec

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Defining formula

{\displaystyle{\displaystyle!}}

introduction.Sx4.p1.t1.r15.m5addec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3abkdec

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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.m2addec

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Defining formula

{\displaystyle{\displaystyle n}}

C10.S1.XMD2.m1fdec

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