On the Relation between Lambert W-Function and Generalized Hypergeometric Functions

Pushpa Narayan Rathie and Luan Carlos de Sena Monteiro Ozelim ()
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Pushpa Narayan Rathie: Department of Statistics, University of Brasilia, Brasília 70910-900, Brazil
Luan Carlos de Sena Monteiro Ozelim: Department of Civil and Environmental Engineering, University of Brasilia, Brasília 70910-900, Brazil

Stats, 2022, vol. 5, issue 4, 1-9

Abstract: In the theory of special functions, finding correlations between different types of functions is of great interest as unifying results, especially when considering issues such as analytic continuation. In the present paper, the relation between Lambert W-function and generalized hypergeometric functions is discussed. It will be shown that it is possible to link these functions by following two different strategies, namely, by means of the direct and inverse Mellin transform of Lambert W-function and by solving the trinomial equation originally studied by Lambert and Euler. The new results can be used both to numerically evaluate Lambert W-function and to study its analytic structure.

Keywords: Lambert W-function; H-function; R-function; Mellin transform; Lagrange’s inversion theorem (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:gam:jstats:v:5:y:2022:i:4:p:72-1220:d:981467

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