Summation of divergent series by order dependent mappings: Application to the anharmonic oscillator and critical exponents in field theory

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Abstract
We study numerically a method of summation of divergent series based on an order dependent mapping. We consider the example of a simple integral, of the ground‐state energy of the anharmonic oscillator and of the critical exponents of φ34 field theory. In the case of the simple integral convergence can be rigorously proven, while in the other examples we can only give heuristic arguments to explain the properties of the transformed series. For the anharmonic oscillator we have compared our results to an accurate numerical solution (10−23) of the Schrödinger equation. For the critical exponents we have verified the consistency of our results with those obtained before from methods using a Borel transformation.