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Jun
6
comment Asymptotic of a sum evaluation as $ x \to \infty $
why not ?, what i have made wrong in my approximation
Jun
5
comment Solve the Sturm-Liouville problem $y'' + λy = 0$ given $y(0) = 0$, $y'(6) = 0$?
for the firste term the solution is $ y(X)=Asin( \sqrt{\lambda}x $ so $ B=0$ and $ y(0)=0 $ . The quantization condition comes from the secon equation $ y'(6)=0= \sqrt{\lambda}cos( \sqrt{\lambda} 6) $
May
30
comment $\psi(p_{n+1}) - \psi(p_n)$?
with the prime number theorem on mind $ \Psi (x) \to 0 $ so for big primes the different will be about $ \p_{n+1}-p_{n} $ but again in prime number theorem $ p_{n} \to nlog(n) $ so we have that $ S(p_{n}) \to 1+log(n) $
May
29
comment an implicit solution is valid to show that the solution exists??
wel if you lik put $ y^{-1}(x)=x(y)$ but i have always written this way with the minus 1
May
29
comment an implicit solution is valid to show that the solution exists??
i have said that the solution to a certain differential equation $ y^{-1}(x)=x+g(X) $ but g(x) is known the unknon is $ y(x) $
May
29
comment Euler product for Riemann zeta and analytic continuation
the question IS : can we use borel transform to make an analytic continuation of the Euler product ?
May
26
comment Gram's series for integral equation
if someone wants to look my solution of the integral equation of first kind vixra.org/abs/1304.0013 i extend GRAM SERIES to other integral equations as well
May
26
comment Integral equation solution in power series
i know how to solve it with the foruier tranfsorm of course i was asking if there is another method to solve this integral equation for example by power series
May
23
comment Is it possible that $\pi$ is finite in other numerical bases?
PI is an integer in basis $ \Pi $ by trivial definition and if we allow non integer basis
May
23
comment Is a proof still valid if only the writer understands it?
a TRUTH is a truth even if only a person understand
May
21
comment orthogonal polynomials and quadrature formulae
OK thanks good point
Apr
28
comment Mathematicians ahead of their time?
FOURIER invented the general method but i think that euler and bernoulli had used the fouire method to the solution of the string problem :D
Apr
28
comment Mathematicians ahead of their time?
RAMANUJAN and EULER .. Euler invented things like Borel transform FOurier analysis , Laplace transform and many other ideas which were studied hundred years after
Apr
28
comment Ordinary Differential Equations ODEs Solve the Initial Value Problem
$ e^{Mt}=1+Mt+\frac{t^{2}M^{2}}{2}+\frac{t^{3}M^{3}}{6}+..$
Mar
29
comment Why is $\zeta(s)\neq0$ for $\operatorname{Re}(s)=0$?
PRIME NUMBER THEOREM: riemann zeta function has no zeros of the form $ 1+it$ for real t therefore from the functional equation the riemann zeta function has no zeros of the form $ 0+it $
Mar
23
comment laurent series of a function defined by an integral
and for some $ |x| > 1 $ i mean an asymptotic Laurent series valid as $ x \to \infty $ thanks
Mar
23
comment laurent series of a function defined by an integral
assume all that you need :D let us suppose taht teh function can be defined for complex 'x' and so on
Mar
23
comment laurent series of a function defined by an integral
well assume that for every $ x >0 $ the integrals F(X) and H(X) exists :D
Mar
23
comment laurent series of a function defined by an integral
$ g(t) $ is smooth with no poles so the integral exists for every 'x' since there are no poles in the integrand
Mar
19
comment Real roots plot of the modified bessel function
OK thanks in fact i managed to prove that the roots of the function (smooth part) was about $ \frac{ \sqrt{E}}{2\pi}log(\frac{\sqrt{E}}{2\pi e}) $ that's why i thought that the zeros would be related