Definition:Binomial Series
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Definition
Consider the Binomial Theorem, which in one of its various forms is given here:
- $\paren {1 + x}^\alpha = 1 + \dbinom \alpha 1 x + \dbinom \alpha 2 x^2 + \dbinom \alpha 3 x^3 + \cdots$
for arbitrary real $\alpha$.
The above infinite series is known as the binomial series.
Also see
- Results about binomial coefficients can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): binomial series
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): binomial theorem
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): binomial series
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): binomial theorem