What is the value of this finite sum?

In summary, the conversation is about a complicated sum involving hypergeometric series and the speaker is looking for resources to better understand it. They mention a specific sum and provide its formula, along with their limited knowledge of the topic. The other person suggests a book and online resources for further reading.
  • #1
Pere Callahan
586
1
Hi,

I came across a somewhat unwieldy sum which I do not know how to manipulate any further. I suspect it might have something to do with a hypergeometric series, but I am not sufficiently familar with those series to be able to just see how it might be related to them.

The sum in question is

[tex]\sum_{1\leq r_1< r_2 < \dots < r_n \leq m}{\frac{ (k-1)!(k-2r_1)!(k-2r_2+1)! \dots (k-2r_{n-1}+n-2)!(k-2r_n+n-1)! }{ (k-2r_1+1)!(k-2r_2+2)! \dots (k-2r_{n-1}+n-1)!(k-2r_n+n)! }}[/tex]

where k is some non-negative integer, [tex]0\leq n \leq k[/tex]. m is defined by

[tex]m=\left\lfloor\frac{k+n}{2}\right\rfloor \geq n[/tex].

Do you know of any books where I could look up things like that?

Any help is greatly appreciated.

-Pere
 
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  • #3
Thanks. A=B seems to be an intersting book, I hadn't heard of it before.
 

FAQ: What is the value of this finite sum?

What is a finite sum?

A finite sum is a mathematical calculation that involves adding a finite number of terms together. It is represented by the symbol ∑ and can be written as ∑i=1n ai, where n is the number of terms and ai represents each individual term.

Why is the value of a finite sum important?

The value of a finite sum is important because it allows us to find the total value of a set of numbers or quantities that are added together. It can also help us understand patterns and relationships between numbers.

What is the formula for calculating the value of a finite sum?

The formula for calculating the value of a finite sum is: ∑i=1n ai = a1 + a2 + ... + an, where n is the number of terms and ai represents each individual term in the sum.

How is a finite sum different from an infinite sum?

A finite sum involves a finite number of terms, while an infinite sum has an infinite number of terms. In other words, a finite sum has a specific and limited number of terms, while an infinite sum continues on indefinitely.

What are some real-life applications of finite sums?

Finite sums have various applications in fields such as finance, economics, and physics. For example, they can be used to calculate the total cost of a set of expenses, determine the total revenue from a series of sales, or find the total distance traveled by an object with varying speeds.

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