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Sep
6
comment How to find asymptotics?
should a taylor series near $ x=0 $ work ??
Aug
29
comment Laurent expansion of $ \log\zeta(s) $
perhaps if we could prove that (approximately) $ log\zeta (s) \sim -log(1-1/s) $ then we would have the expansion $log\zeta (s) \approx \sum_{n=1}^{\infty} \frac{1}{ns^{n}}$
Aug
19
comment Laurent expansion of $ \log\zeta(s) $
mistake corrected, the idea is to expand the logarithm of riemann zeta $ log\zeta (s) $ as a Z-transform , see en.wikipedia.org/wiki/Z_transform
Aug
7
comment What are applications of number theory in physics?
zeta regularization $ 1+2^{k}+3^{k}+....$ understood as $ \zeta (-k) $ appears whenever trying to regularize series and integrals :) that are divergents
Jul
29
comment abel summation and Harmonic series
no, you are wrong is $ log(1-e^{-\epsilon}) 4 not $ log(1+\epsilon) $
Jul
18
comment Laguerre transform function
for non integer 'm' we can use fractional derivative to define $ L_{m}(x)= \frac{e^{x}}{\Gamma (m+1)}D_{x}^{n}(x^{n}e^{-x}) $
Jul
11
comment zero raised to infinity
$ o^{0}=1 $ since $ x^{x}=e^{xln(x)} $ and $ x \to 0 $ $ xln(x)=1 $
Jul
6
comment Computing the value of logarithmic series: $Q(s,n) = \ln(1)^s + \ln(2)^s + \ln(3)^s + \cdots+ \ln(n)^s $
the sum is divergent , regularizatio is needed so $ (-1)^{s}\zeta ^{(s)} (0) $
Jul
6
comment Calculate $ \int_{\mathbb{R}} \frac{dx}{x^4+1}$ using the residues theorem.
Ramanujan's master theorem is easier :) mathworld.wolfram.com/RamanujansMasterTheorem.html
Jul
4
comment Question on Differential forms
$ curl(graf)= 0 $ for example perhaps if $ w^{1}= \frac{\partial f}{\partial x} $ and $ w^{2}= \frac{\partial f}{\partial y} $
Jul
4
comment Is it possible to use regularization methods on the Harmonic Series?
you can use the regulator $ R(n,s)= \frac{n^{s}+n^{-s}}{2}$ so the series $ \sum_{n=1}^{\infty}R(n,s)n^{-1} $ converges to the Euler-Mascheroni constant in the limit $ s \to 0 $
Jul
2
comment Harmonic series principal value
$ \zeta (1+s)= \frac{1}{s}+ \gamma $ , $ \zeta (1-s)= \frac{1}{-s}+ \gamma $ so the sum gives $ \zeta (1+s)+ \zeta (1-s)= 2\gamma$ in the limit $ s \to 0 $
Jun
26
comment Would be this formula valid ? Zeta regularization and Euler product plus zeros.
@OL the product over m gives your fucntion but we mus also include a product over primes
Jun
26
comment Proving $\left\| \frac{\vec{v}}{\|\vec{v}\|}\right\| =1$, $\vec{v}\ne \vec{0}$
your expression is NOT a vector since a vector divided by an scalar is just another vector
Jun
26
comment Multiplication $ H\times P(1/x) $ in sense of distributions
Cauchy's principal value en.wikipedia.org/wiki/Cauchy_principal_value
Jun
24
comment Mellin transform of digamma function
i have used RAMANUJAN MASTER THEOREM and it is much more easier and faster however i aked if this can be obtained by another methods.
May
27
comment Logarithmic Equations
take the 3/4 power in both sides $ (5x+2)= 16^{3/4}=8 $ (use calculator) :) then $ 5x=8-2 $ and $ x=6/5 $
May
25
comment Summation with factorial terms (involving Laguerre polynomials)
rewrite $ x^{k } $ as a linear combination of Laguerre polynomials $ L_{m} (x) $ and use the orthogonality property $ \int_{0}^{\infty} L_{m}(x)L_{n}(x)exp(-x)dx =0 $
May
24
comment numerical approximation to logarithm
OK you are right perhapsh i should use this expression plus a power series involving teh difference $ln(x+1)-ln(x) $
May
23
comment numerical approximation to logarithm
so my expression should be $ ln(x)= x\int_{0}^{1} \frac{dt}{1+xt} $