Hypergeometric representations of Gelfond's constant and its generalisations

Arjun K. Rathie; Gradimir V. Milovanović; Richard B. Paris

Hypergeometric representations of Gelfond's constant and its generalisations

Arjun K. Rathie, Gradimir V. Milovanović, Richard B. Paris

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Abstract

The aim of this note is to provide a natural extension and generalisation of the well-known Gelfond constant e^π 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.

Original language	English
Pages (from-to)	71-77
Number of pages	7
Journal	Matematicki Vesnik
Volume	74
Issue number	1
Early online date	31 Dec 2021
Publication status	Published - 1 Mar 2022

Keywords

Gelfond's constant
Hypergeometric function
Gauss summation theorem

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Paris_HypergeometricRepresentationsOfGelfond'sConstant_Published_2022Final published version, 339 KBLicence: CC BY

http://www.vesnik.math.rs/vol/mv22107.pdfLicence: CC BY

Cite this

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abstract = "The aim of this note is to provide a natural extension and generalisation of the well-known Gelfond constant eπ 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.",

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AB - The aim of this note is to provide a natural extension and generalisation of the well-known Gelfond constant eπ 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.

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Hypergeometric representations of Gelfond's constant and its generalisations

Abstract

Keywords

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