Wikipedia:Reference desk/Archives/Mathematics/2007 September 16

= September 16 =

What does this mean?
I came across this in an (non-wikipedia) article. I have no idea what it means.

$$\Sigma \, t^3 = \frac{t^4}{4}-\frac{t^3}{2}+\frac{t^2}{4}$$

Can someone explains what it actually means. 220.237.181.98 01:57, 16 September 2007 (UTC)


 * Which article? I don't know a meaning. Perhaps it is a failed attempt to write the summation
 * $$\sum_{x=1}^t x^3 = \left(\frac{t(t+1)}{2}\right)^2 = \frac{t^4}{4}+\frac{t^3}{2}+\frac{t^2}{4}$$
 * PrimeHunter 03:37, 16 September 2007 (UTC)


 * No, it's definately minus t cube on two which is $$-\frac{t^3}{2}$$ . There is no typo. 220.237.181.98 04:45, 16 September 2007 (UTC)


 * If you shift the index by 1, then you get what you want. So maybe it is a failed attempt to write this
 * $$\sum_{x=1}^{t-1} x^3 = \left(\frac{t(t-1)}{2}\right)^2 = \frac{t^4}{4}-\frac{t^3}{2}+\frac{t^2}{4}$$
 * --Spoon! 05:52, 16 September 2007 (UTC)


 * Can you give us some more context? What was the article about? Maelin (Talk | Contribs) 05:02, 16 September 2007 (UTC)


 * The article is entitled "The Difference Calculus". It's about a collection of mathematical tools for solving difference equations. At least that is what it says. 211.28.126.201 09:19, 16 September 2007 (UTC)


 * Could you provide a link or other info on where to find it? —Bromskloss 11:47, 16 September 2007 (UTC)


 * Perhaps they are showing how to solve the recurrence relation $$a_{t+1} = a_t + t^3$$ --Spoon! 15:20, 16 September 2007 (UTC)


 * I don't know the article, but in this context Σ and Δ are possibly operators turning functions on integers into other functions on integers, defined as follows. If F is defined on the integers, then the forward difference ΔF is the function f such that f(t) = F(t+1) – F(t). For example, if F(t) = t4 – 2t3 + t2, then (ΔF)(t) = 4t3. The operator Σ is such that if Σf = F, then ΔF = f. This allows an indefinite summation constant for Σ, which can be fixed by agreeing that (Σf)(0) = 0. Other definitions are possible; in particular the "backward difference" (∇F)(t) = F(t) – F(t–1). See also Difference operator.  --Lambiam 18:47, 16 September 2007 (UTC)


 * I agree with Lambiam, it must be the summation operator as defined in Knuth's Concrete Mathematics. &#x2013; b_jonas 21:10, 17 September 2007 (UTC)