DLMF:33.6.E5 (Q9537)

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Language	Label	Description	Also known as
English	DLMF:33.6.E5	No description defined

Statements

{\displaystyle{\displaystyle{H^{\pm}_{\ell}}\left(\eta,\rho\right)=\frac{e^{% \pm\mathrm{i}{\theta_{\ell}}\left(\eta,\rho\right)}}{(2\ell+1)!\Gamma\left(-% \ell\pm\mathrm{i}\eta\right)}\left(\sum_{k=0}^{\infty}\frac{{\left(a\right)_{k% }}}{{\left(2\ell+2\right)_{k}}k!}(\mp 2\mathrm{i}\rho)^{a+k}\left(\ln\left(\mp 2% \mathrm{i}\rho\right)+\psi\left(a+k\right)-\psi\left(1+k\right)-\psi\left(2% \ell+2+k\right)\right)-\sum_{k=1}^{2\ell+1}\frac{(2\ell+1)!(k-1)!}{(2\ell+1-k)% !{\left(1-a\right)_{k}}}(\mp 2\mathrm{i}\rho)^{a-k}\right),}}

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DLMF:33.6.E5

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