A note on interpolation series in the complex domain

TL;DR

This paper introduces a complex-analytic interpolation method that generalizes Newton, Taylor, and Laurent formulas, providing an effective identity theorem for holomorphic functions in complex domains.

Contribution

It develops a unified interpolation framework in the complex domain that extends classical polynomial and Laurent series methods.

Findings

Provides a new interpolation identity for holomorphic functions.

Generalizes classical Taylor and Laurent formulas.

Establishes an effective identity theorem for complex domains.

Abstract

Given a convergent sequence of nodes we present a one-dimensional-holomorphic-function version of the Newton interpolation method of polynomials. It also generalises the Taylor and the Laurent formula. In other words, we present an effective identity theorem for complex domains.