A note on Coulomb scattering amplitude

The summation of the partial wave series for Coulomb scattering amplitude, $f^C(\theta)$ is avoided because the series is oscillatorily and divergent. Instead, $f^C(\theta)$ is obtained by solving the Schr{\"o}dinger equation in parabolic cylindrical co-ordinates which is not a general method. Here, we show that a reconstructed series, $(1-\cos\theta) ^2f^C(\theta)$, is both convergent and analytically summable.