Abel sum

Noun

(mathematical analysis) Given a power series f(x)=∑ₙ₌₀ ᪲a_nxⁿ that is convergent for real x in the open interval (0, 1), the value lim _(x→1⁻)∑ₙ₌₀ ᪲a_nxⁿ, which is assigned to f(1)=∑ₙ₌₀ ᪲a_n by the Abel summation method (or A-method).

Japanese Meaning

Abel和（エイベルわ）：数学解析における和の定義の一種。具体的には、冪級数 f(x)=∑ₙ₌₀∞ aₙxⁿ が (0,1) の区間で収束するとき、x→1⁻ の極限 limₓ→1⁻∑ₙ₌₀∞ aₙ xⁿ により f(1) が定義される手法を指す。

What is this buttons?

For the power series f(x)=∑_{n=0}^∞ a_n x^n that converges for 0<x<1, the Abel sum is defined as lim_{x→1^-} ∑_{n=0}^∞ a_n x^n and is assigned to f(1) by the Abel summation method.

Google Translation / DeepL Translation

冪級数 f(x)=∑_{n=0}^∞ a_n x^n が 0

Details

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