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Transactions of the American Mathematical Society

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The $ p$-adic log gamma function and $ p$-adic Euler constants

Author: Jack Diamond
Journal: Trans. Amer. Math. Soc. 233 (1977), 321-337
MSC: Primary 12B40; Secondary 33A15
MathSciNet review: 0498503
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Abstract: We define $ {G_p}$, a p-adic analog of the classical log gamma function and show it satisfies relations similar to the standard formulas for log gamma. We also define p-adic Euler constants and use them to obtain results on $ G{'_p}$ and on the logarithmic derivative of Morita's $ {\Gamma _p}$.

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Keywords: Log gamma function, Euler constants, p-adic functions
Article copyright: © Copyright 1977 American Mathematical Society

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