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Reference.org
p-adic gamma function
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the <i>p</i>-adic gamma function Γ<i>p</i> is a <a href="/facts/Function_(mathematics)/CdReEKCh">function</a> of a <a href="/facts/P-adic/SDgDbkLF"><i>p</i>-adic</a> variable analogous to the <a href="/facts/Gamma_function/SjGQcnyw">gamma function</a>. It was first explicitly defined by Morita (1975), though Boyarsky (1980) pointed out that Dwork (1964) implicitly used the same function. Diamond (1977) defined a <i>p</i>-adic analog <i>G</i><i>p</i> of log Γ. Overholtzer (1952) had previously given a definition of a different <i>p</i>-adic analogue of the gamma function, but his function does not have satisfactory properties and is not used much. </p>