Variational Interpolation Algorithm between Weak- and Strong-Coupling Expansions

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For many physical quantities, theory supplies weak- and strong-coupling expansions of the types ∑ aₙ αⁿ and αᵖ∑ bₙ (α-2/q) ⁿ, respectively. Either or both of these may have a zero radius of convergence. We present a simple interpolation algorithm which rapidly converges for an increasing number of known expansion coefficients. The accuracy is illustrated by calculating the ground state energies of the anharmonic oscillator using only the leading large-order coefficient b₀ (apart from the trivial expansion coefficent a₀=1/2). The errors are less than 0.5 for all g. The algorithm is applied to find energy and mass of the Fröhlich-Feynman polaron. Our mass is quite different from Feynman's variational approach.