Meanings
- algebraAny 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.
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.
2 more 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.
This chapter gives a rigorous development of the algebraic properties of formal power series. Our goal is to extend the familiar operations on polynomial functions (like addition, multiplication, composition, and differentiation) to the setting of formal power series. In certain situations we will even be able to define infinite sums and products of formal power series.[…]In combinatorics, it usually suffices to consider formal power series whose coefficients are integers, rational numbers, or complex numbers.
2011, Nicholas Loehr, Bijective Combinatorics, Taylor & Francis (CRC Press), page 243Synonyms: formal series
Synonyms & antonyms
nounAny 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.
Translations
Bulgarian формален степенен ред
- формален степенен ред (formalen stepenen red)generalization of a power series
French série formelle
- série formellegeneralization of a power series
German formale Potenzreihe
- formale Potenzreihegeneralization of a power series
Hungarian formális hatványsor
- formális hatványsorgeneralization of a power series
Italian serie formale di potenze
- serie formale di potenzegeneralization of a power series
Polish szereg potęgowy formalny
- szereg potęgowy formalnygeneralization of a power series
Romanian serie formală
- serie formalăgeneralization of a power series
Russian форма́льный степенно́й ряд
- форма́льный степенно́й ряд (formálʹnyj stepennój rjad)generalization of a power series
Spanish serie formal de potencias
- serie formal de potenciasgeneralization of a power series
Cite this entry
formal power series. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/formal%20power%20series
“formal power series.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/formal%20power%20series. Accessed November 5, 2026.
WatkinsX Dictionary, s.v. “formal power series,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/formal%20power%20series.
Source: formal power series on Wiktionary, CC BY-SA 4.0.