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FGH, a code for the calculation of Coulomb radial wave functions from series expansions. (English) Zbl 1007.81021

Summary: The code FGH is an up-dated version of a code COULFG [see the author, ibid. 25, 87 (1982)], used for the calculation of the Coulomb functions $f$ and $g$, analytic in the energy, for attractive potentials. The new code works for attractive and repulsive potentials and also gives the functions $h$ which have simple asymptotic forms. There is an option to use either the variables $\left(\epsilon ,r\right)$ customary in atomic physics, or (for positive energies) $\left(\eta ,\rho \right)$ customary in nuclear physics. When $\left(\eta ,\rho \right)$ are used, the code also gives the functions ${F}_{\ell }\left(\eta ,\rho \right)$ and ${G}_{\ell }\left(\eta ,\rho \right)$.

Use of series solutions can lead to loss of accuracy due to cancellation effects. FGH provides an indication of the number of significant figures lost due to cancellations.

##### MSC:
 81Q05 Closed and approximate solutions to quantum-mechanical equations 81-08 Computational methods (quantum theory)
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