Abstract
Using fermionic p‐adic invariant integral on ℤp, we construct the Barnes′ type multiple Genocchi numbers and polynomials. From those numbers and polynomials, we derive the twisted Barnes′ type multiple Genocchi numbers and polynomials. Moreover, we will find the Barnes′ type multiple Genocchi zeta function.
Highlights
Theoretical physicists have devised ultrametric structures similar to tree-like structures arising in the study of physical systems because the fact is that the physical space may no longer be Archimedean seems plausible to some mathematical physicists at a very small distance
Barnes showed that ζN had a meromorphic continuation in s with simple pole only at s 1, . . . , N and defined his multiple gamma function ΓN w in terms of the s-derivative at s 0, which may be recalled here as follows: Ψn w | a1, . . . , aN ∂sζN s, w | a1 . . . , aN | s 0
Theorem 3.1 Property of distribution of Gnr,ε,χ x | w1, . . . , wr
Summary
Theoretical physicists have devised ultrametric structures similar to tree-like structures arising in the study of physical systems because the fact is that the physical space may no longer be Archimedean seems plausible to some mathematical physicists at a very small distance. They have looked for construct-related models using p-adic numbers and p-adic analysis. We study the q-Gnocchi numbers and polynomials in q-type of special generating functions see 1, 2. AN that will be assumed to be positive Barnes showed that ζN had a meromorphic continuation in s with simple pole only at s 1, . . . , N and defined his multiple gamma function ΓN w in terms of the s-derivative at s 0, which may be recalled here as follows: Ψn w | a1, . . . , aN ∂sζN s, w | a1 . . . , aN | s 0
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