Jose Garcia
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 Jul 19 revised Laguerre transform function added 155 characters in body 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 18 asked Laguerre transform function Jul 13 accepted system of differential equations of first order Jul 11 comment zero raised to infinity $o^{0}=1$ since $x^{x}=e^{xln(x)}$ and $x \to 0$ $xln(x)=1$ Jul 11 asked system of differential equations of first order Jul 6 answered I'm looking for several ways to prove that $\int_{0}^{\infty }\sin(x)x^mdx=\cos(\frac{\pi m}{2})\Gamma (m+1)$ 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 $s \to 0$ Jul 2 revised Harmonic series principal value added 1 characters in body Jul 2 asked Harmonic series principal value Jun 28 answered Estimating $\sum_{p_2 \leq x} (\log p_2)^2$ 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 revised Would be this formula valid ? Zeta regularization and Euler product plus zeros. added 5 characters in body Jun 26 asked Would be this formula valid ? Zeta regularization and Euler product plus zeros. 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