Standard Lemma guide

holomorphic

adj · 2 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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No pronunciation record was provided for this word.

1

adj

Meaning 1

Complex-differentiable on an open set around every point in its domain.

Definition source: English Wiktionary via Wiktextract

Usage: not-comparable

Topics: complex-analysis, mathematics, sciences

Examples

  • 1998, Stefan-M. Heinemann, Julia Sets in Cn, Hartje Kriete, Progress in Holomorphic Dynamics, Addison Wesley Longman, page 159, The iteration of holomorphic maps of one variable is one of the most lively fields of current mathematical research. Since its beginning in the twenties of this century, the theory of holomorphic endomorphisms of the Riemann sphere (= rational functions) has become well developed.
  • 1998, Robert Friedman, Algebraic Surfaces and Holomorphic Vector Bundles, Springer, page 303, A holomorphic 1-form on X is closed, and so 0=dη1=df and η2.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

2

adj

Meaning 2

Having holohedral symmetry.

Definition source: English Wiktionary via Wiktextract

Usage: not-comparable

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

From holo- + -morphic.

Across languages

Translations

10 source translations are retained for this English entry.

  • Czech: holomorfní — of a complex function
  • Finnish: holomorfinen — of a complex function
  • French: holomorphe — of a complex function
  • German: holomorph — of a complex function
  • Hungarian: holomorf — of a complex function
  • Kazakh: голоморфтық (golomorftyq) — of a complex function
  • Polish: holomorficzny — of a complex function
  • Portuguese: holomorfo — of a complex function
  • Portuguese: holomorfa — of a complex function
  • Russian: голоморфный (golomorfnyj) — of a complex function
Real reading context

holomorphic in complete knowledge articles