HYPERGEOMETRIC REPRESENTATIONS OF GELFOND'S CONSTANT AND ITS GENERALISATIONS

Authors

  • A. K. Rathie Department of Mathematics, Vedant College of Engineering and Technology, Rajasthan Technical University, Bundi, 323021, Rajasthan, India Author
  • G. V. Milovanović Faculty of Science and Mathematics, University of Niš, 18000 Niš, Serbia Author
  • R. B. Paris Division of Computing and Mathematics, Abertay University, Dundee DD1 1HG, UK Author

Keywords:

Gelfond's constant, hypergeometric function, Gauss summation theorem

Subjects:

11Y60, 33B10, 33C05, 33C20

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.

Published

2022-01-15

Issue

Vol. 74 No. 1 (2022): Vol. 74, Issue 1

Section

Articles

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