DLMF:13.23.E11 (Q4645): Difference between revisions

Revision as of 16:50, 30 December 2019

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Language	Label	Description	Also known as
English	DLMF:13.23.E11	No description defined

{\displaystyle{\displaystyle\int_{0}^{\infty}e^{\frac{1}{2}t}t^{\frac{1}{2}(% \nu-1)-\mu}W_{\kappa,\mu}\left(t\right)J_{\nu}\left(2\sqrt{xt}\right)\mathrm{d% }t=\frac{\Gamma\left(\nu-2\mu+1\right)}{\Gamma\left(\frac{1}{2}+\mu-\kappa% \right)}\*e^{\frac{1}{2}x}x^{\frac{1}{2}(\mu-\kappa-\frac{3}{2})}\*W_{\frac{1}% {2}(\kappa+3\mu-\nu-\frac{1}{2}),\frac{1}{2}(\kappa-\mu+\nu+\frac{1}{2})}\left% (x\right),}}

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{\displaystyle{\displaystyle\max(2\Re\mu-1,-1)<\Re\nu<2\Re(\mu-\kappa)+\tfrac{% 3}{2}}}

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Revision as of 14:33, 29 December 2019 imported>Admin Admin moved page Main Page to Verifying DLMF with Maple and Mathematica	Revision as of 16:50, 30 December 2019 imported>Admin Admin moved page Main Page to Verifying DLMF with Maple and Mathematica Newer edit →
	Property / constraint
		${\displaystyle{\displaystyle\max(2\Re\mu-1,-1)<\Re\nu<2\Re(\mu-\kappa)+\tfrac{% 3}{2}}}$ `\max(2\realpart@@{\mu}-1,-1)<\realpart@@{\nu}<2\realpart@@{(\mu-\kappa)}+\tfrac{3}{2}`
	Property / constraint: ${\displaystyle{\displaystyle\max(2\Re\mu-1,-1)<\Re\nu<2\Re(\mu-\kappa)+\tfrac{% 3}{2}}}$ / rank
		Normal rank