Recent content by Pere Callahan

So, for this particular recursion, the substitution b[i]\mapsto(i+1)c[i] reduces the equation to a very easy form. The question about the general theory remains.

Hi all, I came across a linear recurrence with polynomial coefficients and realized that I don't have a clue as to how to solve it. The usual methods like generating functions or guessing seem not to work in that case. Here is the equation: i (i - 1) (i - 2) b[i] = 1/3 (i + 1) i (1 -...

Hi, I was wondering if the constant \sum_{n=1}^\infty{2^{-2^n}} has a certain name or some history or anything. It certainly appears not to have a closed form expression. It also certainly has some value because it's majorized by the simple geometric series. It's numerical value is...

I remember from my calc III course that there are some algorithms to determine if a given function's integral is expressible in terms of elementary function. Unfortunately I don't remember the details. Does someone know how to prove for a given function that it will never show up as a...

You can if the function in question happens to be linear. The cosine function is apparently not linear so you can not distribute.

Depends on what f and a are... are you given the function f? Or are you asked to determine a function f such that the relation you wrote down holds true for every x? Or something completely different?

You might want to read up on the distinction between ontogeny and phylogeny (in case you're not yet familiar with it) The development of an individual from a fertilized egg (ontogeny) is a superbly controlled process, also in my opinion far from well understood. The main feature certainly is...

Ex falso quodlibet:smile:

As I understand it homology for chromosomes is defined by phenotypes, not genotypes. So there is a certain region on chromosome A(maternal) coding for blue eyes, and a homologous region on chromosome A(paternal) coding for green eyes. They are two alleles of the same gene, and they are located...

Substituting p = q+u sounds like a good idea. Then use (q+u)(1-q-u) = q-q^2-2qu+u-u^2 = q(1-q)-2qu+u-u^2

His name was Riemann, not reiman.

Why would you expect that? The answer \frac{4}{3}12^{3/2}\pi = 32\sqrt{3}\pi is correct. The volume you consider is NOT the volume of the sphere minus the volume of the cylinder because at the poles the cylinder is not contained in the sphere.

Assuming a normal distribution won't do you any good. The water levels in the aquifer at different days are certainly dependent so you need to model them as a time series. One you have estimated a suitable time series model from your observations, the question of how likely the water level is to...

You're welcome. If you want your final result checked just post it.

You could also write it as a vector equation \vec x''(t) = \left(\begin{array}{cc} 1&1\\1&1\end{array}\right)\vec x(t) and go on from there.