An introduction to univalent function theory and the Bieberb

Continue from this paper

Indexing is not verification. Extracted statements should be checked against the source.

Read the original paper ↗ Search this title Learn what Atlas can verify → Suggest a correction or ask a question →

Abstract

The purpose of this paper is to make an introduction to univalent function theory for readers of any level, assuming only foundational knowledge in real and complex analysis. In particular, we state and proof (with details) important theorems utilised in proving Bieberbach's conjecture, especially those that were missed or merely sketched by other texts on univalent functions. We will finally prove the conjecture following the proof given by Lenard Weinstein in a comprehensive and self-contained

Results & Lemmas (1)

Each result is auto-extracted from the paper via OCR - the math is shown verbatim and may carry occasional transcription artifacts. Click to expand the full statement.

Theorem 4.1.1 Theorem 4.1.1. (Rodrigues Formula) The n-th Legendre Polynomial is given by the following formula

Theorem 4.1.1. (Rodrigues Formula) The n-th Legendre Polynomial is given by the following formula $$P_n(x) = \frac{1}{2^n n!} \frac{d^n}{dx^n} \left[ \left( x^2 - 1 \right)^n \right]$$

✦ 291 explorers have wandered the registry - thanks for stopping by. Tell us what you'd like to see →

Usage & privacy

We use first-party site metrics to improve navigation: page visits, internal clicks, search result counts (not search terms), and approximate active time. A random tab ID groups events for seven days; GPC/DNT turns this off. The separate visitor count uses a self-hosted pseudonymous fingerprint and also respects GPC/DNT.

An introduction to univalent function theory and the Bieberbach conjecture

Continue from this paper

Results & Lemmas (1)