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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