Abstract
The analytical solution of the double-logarithmic integral equation with QCD running coupling describing small-x behaviour of the non-singlet structure function ƒNS(x,Q2) has been found for any cut-off parameter μ. Analytical properties of the solution and a position of the right-most singularity in the complex ρ-plane which determines the asymptotics of ƒNS(x,Q2) at small x have been studied. The asymptotical formula ƒNS(x,Q2) = C1x-λ1{lnκ1(Q2/Λ2) —lnκ1 (μ2/Λ2) + κ1 lnκ1-1(Q2/Λ2)[ψ(1) - ψ(λ1)]} valid if x ≪ 1 and ln(Q2/Λ2) ≫ 1 has been obtained where C1, λ1 are constants, κ1 = g/λ1, λ1 < g = 8/(33 - 2ghf), ghf is a number of active flavours and ψ(ξ) denotes the digamma function.
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