Abstract
Solutions of RG equations for β(α) and α(Q) are found in the class of meromorphic functions satisfying asymptotic conditions at large Q (resp. small α), and analyticity properties in the Q
2 plane. The resulting α
R
(Q) is finite in the Euclidean Q
2 region and agrees well at Q ≥ 1 GeV with the
α
s
(Q).