The \(g\)-inverse and reverse-converse series inverse (Q1072552)

In this interesting paper the author gives various general theorems concerning series inversions. A systematic in-depth study has been carried out by the author to get the clue to certain reverse-converse type problems. The motivation of the present work is the one-way generalized inversion due to \textit{J. P. Singhal} and \textit{S. Kumari} [Indian J. Pure Appl. Math. 13, 907--911 (1982; Zbl 0495.33007)]. Several applications and examples are cited to illustrate the usefulness of the general theorems in number theory, combinatorics and special functions. The concluding part of the paper also raises some unsolved problems.