A Series Representation of Analytically Continuous Complex Functions with Negative Powers

2023 · doi:10.21203/rs.3.rs-3575897/v1
preprint OA: closed CC-BY-4.0
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Abstract

First a proof of Taylor’s Theorem is established by Integration by Parts, and then generalization of the IBPformula to ℂ is used to derive Taylor’s Theorem for Complex numbers 𝑧. A similar method to that which is used toderive Taylor’s Theorem is used to derive a Complex valued series representation similar to the Taylor Series but fornegative powers.

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License: CC-BY-4.0