This preprint gives a self-contained exposition of the Sophomore's Dream, its reflected companion integral, and an explicit absolutely convergent double-series representation for a three-parameter generalization. Version 3.0 supersedes previous Zenodo versions. It corrects and refines the presentation by removing the informal “Nightmare” terminology, clarifying the endpoint convention at x = 0, strengthening the convergence discussion, updating the numerical verification with guard digits, and improving the formulation of the three-parameter generalization.
Yago Isasi Parache (Sat,) studied this question.