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幂级数的和函数

English translation: a function of the sum of a power series


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GLOSSARY ENTRY (DERIVED FROM QUESTION BELOW)
Chinese term or phrase:幂级数的和函数
English translation:a function of the sum of a power series
Entered by: albertdeng
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09:18 Sep 29, 2007
Chinese to English translations [PRO]
Science - Mathematics & Statistics
Chinese term or phrase: 幂级数的和函数
A mathematical term.
albertdeng
Local time: 08:43
a function of the sum of a power series
Explanation:
Two possibilities
1. The function is the number of the terms included in the summation. Given an epsilon there exists an N such that for n > N the difference between the finite sum of N terms and the infinite sum of the series (convergence assumed) is less than epsilon, otherwise not guaranteed for n < N terms included in the summation.

2. That the series is convergent is not the question, the function depends on the variable, say x, in the power series, Sigma a_n x^n.

Selected response from:

franksf
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Summary of answers provided
4power series (function)
Bogoyedov
3a function of the sum of a power series
franksf


  

Answers


7 hrs   confidence: Answerer confidence 3/5Answerer confidence 3/5
a function of the sum of a power series


Explanation:
Two possibilities
1. The function is the number of the terms included in the summation. Given an epsilon there exists an N such that for n > N the difference between the finite sum of N terms and the infinite sum of the series (convergence assumed) is less than epsilon, otherwise not guaranteed for n < N terms included in the summation.

2. That the series is convergent is not the question, the function depends on the variable, say x, in the power series, Sigma a_n x^n.



franksf
Native speaker of: Native in EnglishEnglish, Native in ChineseChinese
PRO pts in category: 32
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10 hrs   confidence: Answerer confidence 4/5Answerer confidence 4/5
power series (function)


Explanation:
You give no context. I think there are two possibilities:
1) all it means is that the function is given by a power series.
"series" already includes the notion of sum. I would translate it simply as "power series" or "power series function"
2) Conceivably, it could be a function given by the sum of two or more power series.

There is no way to tell which is correct without context.



Bogoyedov
Local time: 13:43
Specializes in field
Native speaker of: Native in EnglishEnglish
PRO pts in category: 4
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