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

Author

Listed:
  • Pushpa Narayan Rathie

    (Department of Statistics, University of Brasilia, Brasília 70910-900, Brazil
    These authors contributed equally to this work.)

  • Luan Carlos de Sena Monteiro Ozelim

    (Department of Civil and Environmental Engineering, University of Brasilia, Brasília 70910-900, Brazil
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Pushpa Narayan Rathie & Luan Carlos de Sena Monteiro Ozelim, 2022. "On the Relation between Lambert W-Function and Generalized Hypergeometric Functions," Stats, MDPI, vol. 5(4), pages 1-9, November.
  • Handle: RePEc:gam:jstats:v:5:y:2022:i:4:p:72-1220:d:981467
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    References listed on IDEAS

    as
    1. Krishnaiah, P. R., 1976. "Some recent developments on complex multivariate distributions," Journal of Multivariate Analysis, Elsevier, vol. 6(1), pages 1-30, March.
    2. Dumitru Baleanu & Praveen Agarwal, 2014. "On Generalized Fractional Integral Operators and the Generalized Gauss Hypergeometric Functions," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-5, April.
    Full references (including those not matched with items on IDEAS)

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