Absolutely convergent Lidstone series (Q580532)

\textit{J. D. Buckholtz} and \textit{J. K. Shaw} [J. Math. Anal. Appl. 47, 626-632 (1974; Zbl 0294.30014)] characterized the functions representable by everywhere convergent Lidstone series. This paper gives a similar characterization of the functions that are representable by absolutely convergent Lidstone expansions; this is more explicit than \textit{D. V. Widder}'s condition [Trans. Am. Math. Soc. 51, 387-398 (1942; Zbl 0027.39202)].