Abstract
In this article, we show how to construct a regular, non-commutative Cauchy kernel for slice regular quaternionic functions. We prove an (algebraic) representation formula for such functions, which leads to a new Cauchy formula. We find the expression of the derivatives of a regular function in terms of the powers of the Cauchy kernel, and we present several other consequent results.
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Colombo, F., Gentili, G. & Sabadini, I. A Cauchy kernel for slice regular functions. Ann Glob Anal Geom 37, 361–378 (2010). https://doi.org/10.1007/s10455-009-9191-7
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DOI: https://doi.org/10.1007/s10455-009-9191-7
Keywords
- Non-commutative and regular Cauchy kernel
- Slice regular quaternionic functions
- Representation formula for regular functions