Last Updated：2025/11/28

(mathematics, mathematical analysis) Any infinite series of the general form ∑ᵢ₌₀ ᪲a_i(x-c)ⁱ.

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power series

Source Word

power series

(mathematics, mathematical analysis) Any infinite series of the general form ∑ᵢ₌₀ ᪲a_i(x-c)ⁱ.

Japanese Meaning

冪級数：中心 c の周りにおける無限項の多項式で、一般形が∑₍ᵢ₌₀₎ aᵢ (x - c)ⁱで表される数学的対象。

To determine the radius of convergence, we analyze the coefficients of the power series centered at c.

収束半径を決定するために、中心 c の冪級数の係数を解析する。

Sense（1）

(mathematics, mathematical analysis) Any infinite series of the general form ∑ᵢ₌₀ ᪲a_i(x-c)ⁱ.

Thus no single choice of z₀ will give a power series expansion of f(z) valid for all z∈ℂ setminus -1,1 even though f is analytic on this set.

power series

（ plural ）