Complex Analysis

Lars V. Ahlfors, C. A. (1979). Complex Analysis: an introduction to the theory of analytic functions of one complex variable. McGraw-Hill.

Type

Book chapter

Intellectual base

Textbook

Year

1979

ISBN

9780070006577

Link

https://www.mheducation.com/highered/product/complex-analysis-ahlfors.html

Cited by

8 citations across 8 artifacts.

Domain-specific

• Cauchy's integral formula
  • If a function is holomorphic on and inside a positively oriented closed contour, its value at an interior point equals one over two-pi-i times the contour integral of f(z) divided by z minus a; higher powers yield derivatives.
• Complex conjugate
  • The complex conjugate of \(z=a+bi\) is \(\overline z=a-bi\); equivalently, complex conjugation is the unique nontrivial field automorphism of \(\mathbb C\) that fixes every real number.
• Harmonic conjugate
  • The relation is oriented: if (v) is conjugate to (u), then (-u), not (u), is conjugate to (v).
• Lacunary value
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Linear fractional transformation
  • Linear fractional transformation is an invertible map represented by a ratio of two linear expressions, including Mobius transformations over suitable scalar or algebraic settings.
• Monogenic function
  • … limit, derivative value, pointwise versus neighborhood or domain-wide scope, openness and holomorphic analyticity consequence and distinction from polygenic and Clifford-analysis usage are explicit. to An applied instance preserves the invariant under changed notation, scale, dataset, jurisdiction, or implementation..
• Residue (complex analysis)
  • Residues require an isolated singularity and a declared orientation; removable, pole and essential cases use the same coefficient definition.
• Schwarz triangle function
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.

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