  Herein, we present analytical solutions for the electronic energy eigenvalues
of the hydrogen molecular ion H2+, namely the one-electron two-fixed-center
problem. These are given for the homonuclear case for the countable infinity of
discrete states when the magnetic quantum number m is zero. In this case, these
solutions are the roots of a set of two coupled three-term recurrence
relations. The eigensolutions are obtained from an application of EXPERIMENTAL
MATHEMATICS using Computer Algebra as its principal tool and are vindicated by
numerical and algebraic demonstrations. Finally, the mathematical nature of the
eigenenergies is identified. The eigenenergies are related to a generalization
of the Lambert W function.
