P-adic gamma function

In mathematics, the p-adic gamma function Γ_p(s) is a function of a p-adic variable s analogous to the Gamma function, introduced by Morita (1975).

Definition

The p-adic gamma function is the unique continuous function of a p-adic integer s such that

$\Gamma _{p}(s)=(-1)^{s}\prod _{0<i<s,p\not {|}i}i$

for positive integers s.

References

• Morita, Yasuo (1975), "A p-adic analogue of the Γ-function", Journal of the Faculty of Science. University of Tokyo. Section IA. Mathematics, 22 (2): 255–266, ISSN 0040-8980, MR0424762