Pade Approximants and Perturbation Expansions

Pade Approximants and Perturbation Expansions.—The [P/Q] Pade approxi-mant108 109 to a Taylor series T(x) of order M is defined by 

Let us consider these two modifications of a given zero-order operator, that is a uniform displacement of the zero-order energy spectrum and a uniform change of scale in the spacing of the zero-order energy levels. Consider the zero-order operator 

Brandow, in Effective Interactions and Operators in Nuclei , ed. B. R. Barratt, Springer-Verlag, Berlin, 1975. 

Essentials of Pad6 Approximants , Academic Press, New York, 1975. 

Note that when the perturbation parameter is put equal to unity the total hamiltonian operator is recovered, i.e. 

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