Self-similar interpolation in high-energy physics

A method is suggested for interpolating between small-variable and large-variable asymptotic expansions. The method is based on self-similar approximation theory resulting in self-similar root approximants. The latter are more general than the twosided Padé approximants and modified Padé approximants, including these as particular cases. Being more general, the self-similar root approximants guarantee the accuracy that is not worse, and often better, than that of the Padé approximants. The advantage of the root approximants is in their unambiguous definition and in the possibility of their construction, even when Padé approximants cannot be defined. Conditions for the unique definition of the root approximants are formulated. Several examples from high-energy physics illustrate the method. PACS numbers: 02.30.Lt, 02.30.Mv, 02.60.Gf, 03.65.Db, 05.10.Cc, 11.10.Jj, 11.15.Tk, 11.25.Pm ∗corresponding author: V.I. Yukalov E-mail: [email protected]