Limit analysis for binomial series raised to 0 < fractional exponent < 1

Asked Jun 22 '16 at 09:35

Active Jun 22 '16 at 09:35

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I am trying to expand a series and trying to find a limit analysis:

(1+x)^a

where 0 < a < 1.

I understand that a possible expansion is:

1 + ax + a(a-1)(x^2)/(2!) + a(a-1)(a-2)(x^3)/(3!) +...

What about for fractional values of a? How can I find the limits for which a is for a particular number 0 < a < 1?

asked Jun 22 '16 at 09:35

Corse

expansion remains the some , but it becomes an infinite expansion , (for natural numbers it does not happen as after some terms , remaining become $0$) – avz2611 Jun 22 '16 at 09:41
We generally neglect higher terms – Archis Welankar Jun 22 '16 at 11:08
@avz2611 I see, which terms onwards should I neglect? say power = 2 onwards? how to decide? – Corse Jun 23 '16 at 01:52
@Archis any idea? – Corse Jun 23 '16 at 01:52
When $a-2$ arrives those terms become 0 – avz2611 Jun 23 '16 at 02:19
meaning to say, i could ignore x^3 onwards? – Corse Jun 23 '16 at 06:37

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