Recent content by rscosa

Hi!, there are many other representations (wikipedia or www.mathworld.com) but maybe non of them will be enough helpfull.

Hi!, there is NOT an official proof but many people is trying hard.

Hi! if you are undergraduate or even if you are PhD (as I am) and you read those paper you can become crazy, if you do not then for sure you need a big bottle of aspirines :). By the way I read them and I am alive and not enough crazy!

Hi! I suggest you to read more before publish your problems since this is a very well known question (Wikipedia).

Hi! it is impossible to find a explicit expression for the solutions of you equation because that means that you can solve the integral x^x which is impossible to express in tems of elementary functions (read wikipedia about this topic) so the answer is: You only can get numerical approximation...

Hi! Something like: L_n=L_{n-2}+L_{n-3} with L_0=0, L_1=2, L_3=3 also called the Perrin sequence.

Hi! the answer to this question, IMPOSSIBLE, because you don't have the whole number in memory but just an approximation of PI, so you can get a very acurate approximation of the approximation of PI :).

Hi, I think the problem is not well-defined, the first part is a functional and the second a function. Please, be more especific. But I guess there is some relation like this.

Hi, The answer is described ad a hyper-surface of dimension 2 except if you are talking about a diophantic equation over the integers, please be more especific.

Hi! The Riemann Hypothesis clames that if RZF(z)=0 and z is not a trivial zero, then Re(z)=1/2. That is all. The real part of z needs to be equal to 1/2 (there is NOT restriccion about the imaginary part of z). And 0=0+0 I=ZERO. RFZ= Riemann Zeta function.

Hi! I can not help you with the part of $\psi$ function but yes with the other part. It is well known that x^{n}-1=\prod_{d|n}\Phi_d(x), where \Phi_d is the dth-ciclotomic polynomial which has degree \phi(d), in other words, the euler function of d, so know (a) should be striagtforward...

Hi! the answer of this problem is not known yet. I know the answer if you are in a line at some point and you want to know the probability to return to 0 which can be written in terms of the hyperbolic sine by using really complicated mathematics (not for undergraduates).

Hi! I think your conjecture is wrong although to find a counterexample you need to go so so far away. The Fibonacci sequence satisfies the recurrence relation: $F_n=F_{n-1}+F_{n-2}$ with $F_1=1$ (or $0$ depends how you define it but it does not matter). Now, if you consider the recurrence...

Hi! fortunately all the complex zeros outside of the known strip are negative and even integers, so of course all of them are (complex but real) zeros of the RZF and have the same imaginary part (equal to zero). But the RZF has no zeros with nonzero imaginary part outside of the strip $0<\re...