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 the self-similar approximation theory resulting in self-similar root approximants. The latter are more general than the two-sided Pad\'e approximants and modified Pad\'e approximants, including these as particular cases. Being more general, the self-similar root approximants guarantee an accuracy that is not worse---and is often better---than that of the Pad\'e approximants. The advantage of the root approximants is in their unambiguous definition and in the possibility of their construction, even when Pad\'e approximants cannot be defined. Conditions for the unique definition of the root approximants are formulated. Several examples from high-energy physics illustrate the method.