Abstract

The aim of this note is to provide a natural extension and generalisation of the well-known Gelfond constant $e^\pi$ using a hypergeometric function approach. An extension is also found for the square root of this constant. Several known mathematical constants are also deduced in hypergeometric form from our newly introduced constant.

Keywords: Gelfond's constant; hypergeometric function; Gauss summation theorem.

MSC: 11Y60, 33B10, 33C05, 33C20

Pages:  71$-$77     

Volume  74 ,  Issue  1 ,  2022