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 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.
    Original languageEnglish
    Pages (from-to)71-77
    Number of pages7
    JournalMatematicki Vesnik
    Volume74
    Issue number1
    Early online date31 Dec 2021
    Publication statusPublished - 1 Mar 2022

    Keywords

    • Gelfond's constant
    • Hypergeometric function
    • Gauss summation theorem

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