A note on the Epstein-Hubbell generalized elliptic-type integral (Q1892077)

The main object of this note is to present a remarkably simple derivation of the explicit representation of the Epstein-Hubbell generalized elliptic-type integral as a Gauss hypergeometric function of argument \(k^ 4\). The method applied here is based upon rather elementary formulas, and (unlike the earlier derivations) it does not make use of complex integration with or without residues. It is also pointed out how this method can be applied mutatis mutandis in substantially more general cases.