Rational generalized Stieltjes functions

Abstract

The rational meromorphic functions on $\mathbb{C}\backslash\mathbb{R}$ are studied. We consider the some classes of one, as the generalized Nevanlinna $\mathbf{N}_{\kappa}$ and generalized Stieltjes $\mathbf{N}_{\kappa}^{k}$ classes. By Euclidean algorithm, we can find indices $\kappa$ and $k$, i.e. determine which class the function belongs to $\mathbf{N}_{\kappa}^{k}$.

Keywords

• rational function
• generalized Nevanlinna function
• generalized Stieltjes function

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