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According to (13.4) in Belkic: the trinomial roots, their powers and logarithms from the Lambert series, Bell polynomials and Fox–Wright function https://d-nb.info/1176090631/34

the solution of

Solve[x == 1 + t x^n, x]

is called confluent Fox-Wright function with four parameters(a particular case of Fox-H function). Solve is unaware of this. Is this special function implemented at all, under some name? The closest I came up with is Hypergeometric1F1, but that has only two parameters

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    $\begingroup$ There have already been similar posts and answers here, see mathematica.stackexchange.com/a/202201/9469 $\endgroup$
    – yarchik
    Commented Nov 28, 2020 at 6:37
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    $\begingroup$ Also, The case of integer exponents is discussed in this post here, the case of arbitrary real exponents is discussed in this post on mathoverflow. $\endgroup$
    – yarchik
    Commented Nov 28, 2020 at 6:40

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