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Assuming that: (l), the potential V(z)→z-n(n>2) as z→0; (2), V is regular in Re z>0; (3), V(z)z2→0 as z→∞ in |arg z|<π/2, the following assertions are proved: (l), the scattering matrix element S is meromorphic in the whole λ plane (λ=l+1/2,l—angular momentum);(2)S-1→O((log|λ|)/|λ|) as λ→∞ in |arg λ|<π/2.
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