Phrase guide

formal power series

noun · 1 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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1

noun

Meaning 1

Any finite or infinite series of the form a_0+a_1x+a_2x2...=∑ia_ixi, where the ai are numbers, but it is understood that no value is assigned to x.

Definition source: English Wiktionary via Wiktextract

Topics: algebra, mathematics, sciences

Examples

  • 1995 Alberto Bertoni, Massimiliano Goldwurm, Giancarlo Mauri, Nicoletta Sabatini, Chapter 5: Counting Techniques for Inclusion, Equivalence, and Membership Problems, Volker Diekert, Grzegorz Rozenberg, The Book of Traces, World Scientific, page 138, Moreover, it is useful to observe that in this case the definition of rational formal power series can be simplified: a f.p.s. r∈Q⟨!⟨z⟩!⟩ is rational if and only if r is the quotient of two polynomials.
  • 1997, Greg Marks, Direct Product and Power Series Formations over 2-Primal Rings, Surender Kumar Jain, S. Tariq Rizvi, Advances in Ring Theory, Springer, page 239, We also show that the ring of formal power series over a 2-primal ring (or even a ring satisfying (PS I)) need not be 2-primal.

Meaning relationships

Synonyms: formal series

Antonyms: none provided

History

Etymology

No etymology was provided for this word.

Across languages

Translations

9 source translations are retained for this English entry.

  • Bulgarian: формален степенен ред (formalen stepenen red) — generalization of a power series
  • French: série formelle — generalization of a power series
  • German: formale Potenzreihe — generalization of a power series
  • Hungarian: formális hatványsor — generalization of a power series
  • Italian: serie formale di potenze — generalization of a power series
  • Polish: szereg potęgowy formalny — generalization of a power series
  • Romanian: serie formală — generalization of a power series
  • Russian: форма́льный степенно́й ряд (formálʹnyj stepennój rjad) — generalization of a power series
  • Spanish: serie formal de potencias — generalization of a power series