Recent content by Nedeljko

I solved the problem.

Somebody has a idea?

By this method I can prove that the function g is infinitely Peano differentiable. It means that there are constants a_i such that for any n holds \lim_{x\rightarrow 0}\frac{g(x)-\sum_{k=0}^n\frac{a_k}{k!}x^k}{x^{n+1}}=0. But, this is necessary and insufficient condition for the infinite...

What if f is not analytic near 0?

Homework Statement If f:R\longrightarrow R is a infinitely differentiable function then the function g:R\longrightarrow R defined as g(x)=\left\{ \begin{array}{ll} \frac{f(x)-\sum_{k=0}^n\frac{f^{(k)}(0)}{k!}x^k}{x^{n+1}}, & x\neq 0, \vspace{0.5em}\\ \frac{f^{(n+1)}(0)}{(n+1)!}, &...

I proved the stronger form \ln(1+t^a)>\ln^{1-a}2\ln^a(1+t) or equivalently \log_2(1+t^a)>\log_2^a(1+t) and some generalisations.

Does somebody has ideas for proofs or links?

Is there any online source about this topic? I am skillful in general mathematics. About Gauss Legendre formula, how to prove relation between arithmetic-geometric mean and complete elliptic integral of the first kind? I proved that it is equivalent to formula K(\sin^2(2x))\cos^2x=K(\tan^4x)...

I am interesting for mathematical background od fast algorithms for computing number \pi with complete proofs only. More specific, I am interesting for Gauss Legendre algorithm, Borwein algorithm, Ramanujan formulas and Chudnovsky formula.

Let we assume that the observer's motion law is given in inertial system S. The ideas are: 1. Computing the time of inertial system as a function depending on the observer's proper time. 2. Computing values in inertial system S' co-moving with the observer in any fixed moment. 3...

Thank you for your answer to my question. Because the forum software eat one of my previous messages (non saved to local disk) I made the new post in \LaTeX, posted it as PDF with \LaTeX source in the attached zip file. You can use the source for citing without typesetting formulas. I know for...

Can anybody tell me is the computation attached at the first post of this page correct or not and why?

May be we have different understandig (definitions) of the special theory of relativity. I consider the special relativity as the limit case of the general relativity with G=0. What definition you use? Relativistic theory in the flat spacetime?

I am confused now. Is it true or not that the special relativity is limit case of the general relativity with G=0?

I attached my computation in the attachment. The \LaTeX source is in the attached zip file. My question is: Is this computation correct or not? If it is incorrect, why? tiny-tim Special theory of relativity does not include the gravitation. By this reason, the only prediction Mercury's...