Coulomb Functions - 33.7 Integral Representations

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
33.7.E1	${\displaystyle{\displaystyle F_{\ell}\left(\eta,\rho\right)=\frac{\rho^{\ell+1}2^{\ell}e^{\mathrm{i}\rho-(\pi\eta/2)}}{|\Gamma\left(\ell+1+\mathrm{i}\eta\right)|}\int_{0}^{1}e^{-2\mathrm{i}\rho t}t^{\ell+\mathrm{i}\eta}(1-t)^{\ell-\mathrm{i}\eta}\mathrm{d}t}}$ \regCoulombF{\ell}@{\eta}{\rho} = \frac{\rho^{\ell+1}2^{\ell}e^{\iunit\rho-(\pi\eta/2)}}{|\EulerGamma@{\ell+1+\iunit\eta}|}\int_{0}^{1}e^{-2\iunit\rho t}t^{\ell+\iunit\eta}(1-t)^{\ell-\iunit\eta}\diff{t}	${\displaystyle{\displaystyle\Re(\ell+1+\mathrm{i}\eta)>0}}$	CoulombF(ell, eta, rho) = ((rho)^(ell + 1)* (2)^(ell)* exp(I*rho -(Pi*eta/2)))/(abs(GAMMA(ell + 1 + I*eta)))*int(exp(- 2*I*rho*t)*(t)^(ell + I*eta)*(1 - t)^(ell - I*eta), t = 0..1)	Error	Failure	Missing Macro Error	Error	-