Accurate estimates of asymptotic indices via fractional calculus

Abstract

We devise a three-parameter random search strategy to obtain accurate estimates of the large-coupling amplitude and exponent of an observable from its divergent Taylor expansion, known to some desired order. The endeavor exploits the power of fractional calculus, aided by an auxiliary series and subsequent construction of Pad\'e approximants. Pilot calculations on the ground-state energy perturbation series of the octic anharmonic oscillator reveal the spectacular performance.