On a Difference System for Some Mejer's Functions

A System of Difference Equations of 8-Th Order for Some Mejer's Funtions

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In [4] we've considered a difference system connected with some Mejer's funtions, which satisfy to a differential equation of fourth order. Arithmetical applications f these considerations can be found in [5], [6].

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“…Therefore we decided to present here relatively easy case l = 2, α = 1. We apply the same method, as in [4], where was considered the case l = 0, α = 1; arithmetical applications of corresponding results can be found in [5] - [6]. Results for the case α = 0 can be found in [3].…”

“…In other words, this means that (δ + ν) 4 and (δ − ν − 2) 4 can be omit from the left side of respectively (45)and (46).…”

“…In view of (45), W 1 (f 1 , z, ν) belongs to the null-space of the operator (δ + ν) 4 (as linear operator on C[z]), and in the case, when ν ∈ N, this null-space consits of the single element -the zero element in…”

“…In view of (45), W 1 (f 2 , z, ν) belongs to the null-space of the operator (δ + ν) 4 as linear operator on z −ν C (0) , and, if ν ∈ N, then W 1 (f 2 , z, ν) = γ 2 z −ν .…”