Recent content by MAGNIBORO

Solution for problem #1: Let $$\sum 2^{n}x_{2^{n}}=A \; \; \; \, \, \: \: \: \: ,\sum x_{n}=B\; \; \; \, \, \: \: \: \: , \sum 2^{n-1}x_{2^{n}}=C $$ If we assume a ##a_{n}## such that ##A## diverge and ##B## converge we derive to a contradiccion; so: because ##a_{n}## is monotone decreasent, is...

thanks all of you for your comments , i understand that is important that something is a vector space because then can discribe a certain physical phenomenan so i can interpret that all vector space are equivalent in some way ( correct my if I wrong) but other are better to describe certain...

hi I am studying algebra and i have a question. why is important that something is a vector space?, i mean, what implications have? matrix, complex numbers , functions , n-tuples. What do these have in common, apart from being a vector space? why is so important that a certain set of...

this video also is great

i have to view the proof , but the link to the hadamard function , is not just functions based on gamma? like if we define the function $$P(x)=\Gamma (x)\, sin\left ( \frac{\pi }{2}+2\pi x \right )$$ then is a valid extension for factorial but is obvius trivial, why the hadamard function is...

thanks, I Look at the links that you give me. @FactChecker why is so important that a function is analytic and why is so restrictive?. i heard that one can extend the domain of a function (like riemann zeta) in one unique way and maintaining the function analytic property. if i correct, if a...

hi, i was thinking that every function that satisfies the conditions $$f(0)=1$$ $$f(n+1)=(n+1)f(n)$$ could be a generalization of the factorial function, and why the gamma function is the only function that complies with this conditions? I mean why don't exist other functions, or functions...

wolfram alpha is your friend

make the calculation again but this time set the calculator in radians =D if you give the answer -pi/6 don't worry is the same as 5pi/6, because tan(-pi/6)=tan(5pi/6)=1/-√3=-√3/3

$$I = -4 \pi + 8 \int_{0}^{\pi}cos^2(cos(x))\, dx$$ and with Diff Under the Integral Sign we can get the ODE $$\frac{\partial }{\partial a}\left ( \int_{0}^{\pi}cos^2(cos(ax))\, dx \right )=\frac{1-\pi\, sin^2(cos(a\pi))}{a}\, -\, \frac{1}{a} \int_{0}^{\pi}cos^2(cos(ax))\, dx$$ then you can...

evaluate the function as ##f(c,c+1,n)## and check

the function is: $$\int_{0}^{\frac{\pi }{2}}\left ( a \, cos^2(x) +b \, sin^2(x) \right )^{-n}$$

i found the solution, The function was the result of a definite integral. thanks anyway :thumbup::thumbup:

the solution of ##48N^2 - E^2 = -1## has the form $$E=\frac{\left ( 7+\sqrt{48} \right )^k+\left ( 7-\sqrt{48} \right )^k}{2}$$ for k=0,1,2,... (not only the odd numbers) so other number that not has the form of E=... , is not a solution. then because E=4n+3 , we need to discard...

I also tried to make a program (in C) but only work for the first 4 or 5 solutions (1, 337,...) then it Lost the precision and mark wrong solutions =(