Jose Garcia
Reputation
3,112
Top tag
Next privilege 5,000 Rep.
Approve tag wiki edits
Badges
1 9 23
Newest
Impact
~86k people reached

• 0 posts edited
• 0 helpful flags
• 196 votes cast

# 235 Comments

 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} \$