English Dictionary

formal power series

名詞

(mathematics, algebra) 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.

日本語の意味

数学（代数学）において、formal power series（形式的冪級数）とは、係数が数であり、xに具体的な値は代入されない前提で、a₀ + a₁x + a₂x² + … という形の有限または無限の級数を指す。

A formal power series, like a_0 + a_1 x + a_2 x2 + ···, is studied algebraically without assigning any value to x.

形式冪級数、すなわち a_0 + a_1 x + a_2 x^2 + ... の形をした級数は、係数 a_i を数とし x に具体的な値を代入せずに代数的に扱われる。

意味（1）

(mathematics, algebra) 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.

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.

formal power series （ plural ）