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We present a new approach to quantifying pole parameters of single-channelprocesses based on Laurent expansion of partial wave T-matrices. Instead ofguessing the analytical form of non-singular part of Laurent expansion as it isusually done, we represent it by the convergent series of Pietarinen functions.As the analytic structure of non-singular term is usually very well known(physical cuts with branhcpoints at inelastic thresholds, and unphysical cutsin the negative energy plane), we show that we need one Pietarinen series percut, and the number of terms in each Pietarinen series is automaticallydetermined by the quality of the fit. The method is tested on a toy modelconstructed from two known poles, various background terms, and two physicalcuts, and shown to be robust and confident up to three Pietarinen series. Wealso apply this method to Zagreb CMB amplitudes for the N(1535) 1/2- resonance,and confirm the full success of the method on realistic data. This formalismcan also be used for fitting experimental data, and the procedure is verysimilar as when Breit-Wigner functions are used, but with one modification:Laurent expansion with Pietarinen series is replacing the standard Breit-WignerT-matrix form.

A new method for extracting poles from single-channel data based on  Laurent expansion of T-matrices with Pietarinen power series representing the  non-singular part