“binomial series”的概念、定义、翻译、参考文献-科学参考

binomial series

Mathematics

The series

$1 + \frac{α}{1!} x + \frac{α (α - 1)}{2!} x^{2} + \dots + \frac{α (α - 1) \dots (α - n + 1)}{n!} x^{n} + \dots,$

being the Taylor series for the function (1 + x)^α‎. In general, it is valid for −1 < x < 1. In fact, the series converges for complex x with modulus less than 1, but then care is needed interpreting the sum as (1 + x)^α‎ (see branch). If α‎ is a non-negative integer, the expansion is a finite series and so is a polynomial, and then it is equal to (1 + x)^α‎ for all x.

单词	binomial series
释义	binomial series Mathematics The series $1 + \frac{α}{1!} x + \frac{α (α - 1)}{2!} x^{2} + \dots + \frac{α (α - 1) \dots (α - n + 1)}{n!} x^{n} + \dots,$ being the Taylor series for the function (1 + x)^α‎. In general, it is valid for −1 < x < 1. In fact, the series converges for complex x with modulus less than 1, but then care is needed interpreting the sum as (1 + x)^α‎ (see branch). If α‎ is a non-negative integer, the expansion is a finite series and so is a polynomial, and then it is equal to (1 + x)^α‎ for all x.
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