Binomial series

  • Thread starter steven187
  • Start date
176
0
hello all

I thought this might be an interesting question to ask, consider the following series
[tex]\sum_{n=0}^{\infty}\left(\begin{array}{cc}\alpha\\n \end{array}\right)x^{n}=(1+x)^{\alpha}[/tex]
this is known as the binomial series, whats confusing me is that how could this series exist when [tex]\alpha< n[/tex] especially when its a series that adds infinitely
number of terms, from my understanding this [tex]\left(\begin{array}{cc}\alpha\\n \end{array}\right)[/tex] can only be evaluated when [tex]\alpha>n[/tex] please help

thanxs
 
Last edited:

matt grime

Science Advisor
Homework Helper
9,394
3
they are identically zero for n>alpha (assuming alpha is an integer)
 
176
0
hello Matt
well im still confused, what im not understanding is that if

[tex]\left(\begin{array}{cc}\alpha\\n \end{array}\right)=\frac{\alpha !}{n!(\alpha-n)!}[/tex] and [tex]\alpha< n[/tex] then [tex]\alpha-n[/tex] is negetive how could you find the factorial of a negetive

number, and if they were identically equal to zero i couldnt see how this
[tex]\frac{\alpha !}{n!(\alpha-n)!}=0[/tex]
 

matt grime

Science Advisor
Homework Helper
9,394
3
They are *DEFINED* to be zero. Who said that that formula holds for the cases you have a problem with?

there is another way to define the binomial coefficient for non-integer alpha too, it's


a(a-1)(a-2)..(a-n+1)/n!

that is defined for all a and all integer n.
 
176
0
yeah I get what you mean, its just that I couldnt find any site that tells what happens in that sanario so i got really confused anyway

Thanxs Matt
 
Last edited:

Related Threads for: Binomial series

  • Posted
Replies
1
Views
1K
  • Posted
Replies
1
Views
1K
  • Posted
Replies
3
Views
3K
  • Posted
Replies
4
Views
682
Replies
9
Views
12K
  • Posted
Replies
2
Views
2K
  • Posted
Replies
15
Views
2K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads

Top