The paper constructs p-adic incomplete gamma-functions Γ_p(·,r) valid whenever |r|_p=1 using a two-variable p-adic integral transform as an incomplete Mellin transform, extending the 2023 construction that required |r-1|_p<1.
Washington.Introduction to cyclotomic fields, volume 83 of Graduate Texts in Mathematics
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On $p$-adic incomplete Mellin transforms and $p$-adic incomplete gamma-functions
The paper constructs p-adic incomplete gamma-functions Γ_p(·,r) valid whenever |r|_p=1 using a two-variable p-adic integral transform as an incomplete Mellin transform, extending the 2023 construction that required |r-1|_p<1.