Uniqueness of Γ p : the locally analytic case
Cohomologie p-adique, Astérisque, no. 119-120 (1984), pp. 9-15 
@incollection{AST_1984__119-120__9_0,
     author = {Adolphson, Alan},
     title = {Uniqueness of $\Gamma_p$ : the locally analytic case},
     booktitle = {Cohomologie $p$-adique},
     series = {Ast\'erisque},
     pages = {9--15},
     year = {1984},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {119-120},
     zbl = {0552.12009},
     language = {en},
     url = {https://www.numdam.org/item/AST_1984__119-120__9_0/}
}
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Adolphson, Alan. Uniqueness of $\Gamma_p$ : the locally analytic case, dans Cohomologie $p$-adique, Astérisque, no. 119-120 (1984), pp. 9-15. https://www.numdam.org/item/AST_1984__119-120__9_0/

[1] A. Adolphson, "Uniqueness of Γ p in the Gross-Koblitz formula for Gauss sums". Trans. Amer. Math. Soc. (to appear). | MR | Zbl

[2] F. Baldassarri, "Higher p-adic gamma functions and Dwork cohomology", Asterisque (to appear). | MR | Zbl | Numdam

[3] B. Dwork, "A note on the p-adic gamma function", (preprint).