A basic question: What does closed form mean?

  • Thread starter seeker101
  • Start date
  • #1
28
0
A basic question: What does "closed form" mean?

"The point here is that [itex]\sigma[/itex] algebras are difficult but [tex]\pi[/tex] systems are easy: one can often write down in closed form the general element of a [tex]\pi[/tex] system while the general element event of [itex]\mathbf B \mathbf[/itex] is impossibly complicated" - From the "Diffusions" text by Rogers and Williams.

What does closed form mean?
 

Answers and Replies

  • #2
740
13


hard to describe... I guess it's a formula that has a finite nmber of symbols. i know for an infinite geometric series,

[itex]a+ ax + ax^2 + ax^3 + ... = \frac{a}{1-x}[/itex]

the right-hand side is a closed form of the left-hand side
 
  • #3
disregardthat
Science Advisor
1,854
33


I suppose it depends on the context. If you have a sum of infinite terms, "closed form" would perhaps be an explicit formula of a few terms.

Wiki got something on it:

"In mathematics, an expression is said to be a closed-form expression if, and only if, it can be expressed analytically in terms of a bounded number of certain "well-known" functions. Typically, these well-known functions are defined to be elementary functions; so infinite series, limits, and continued fractions are not permitted.

Similarly, an equation or system of equations is said to have a closed-form solution if, and only if, at least one solution can be expressed as a closed-form expression."
 
  • #4
105
0


I don't think it is limited to infinite series.

Say you wanted the sum of 5 powers of 9: 9^4 + 9^3 + 9^2 + 9^1 +9^0

Not so hard, but what if there were a hundred terms?

Note that the sum is 111119. Or 888889/89.

But 888889 is 95-1. For n terms, the closed form would be

(9n-1)/8
 
Last edited:

Related Threads on A basic question: What does closed form mean?

  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
7
Views
12K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
6
Views
3K
Replies
6
Views
1K
  • Last Post
Replies
12
Views
9K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
5
Views
4K
Replies
9
Views
2K
  • Last Post
Replies
6
Views
1K
Top