Jose Garcia
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 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 $ln(x)= x\int_{0}^{1} \frac{dt}{1+xt}$ May 20 comment How to find inverse of the function $f(x)=\sin(x)\ln(x)$ you CAN ALWAYS invert the function numerically , try mathwolframalpha wolframalpha.com/input/?i=%5Cinv%7Bsin%28x%29ln%28x%29%7D May 18 comment Closed form for n-th anti-derivative of $\log x$ kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1692-02.pdf May 10 comment functional equation involving $f(x/k)$ what does 'mathematica softwary' say ?? May 2 comment Differential Equation $y'=4|y|^{3/4}, y(0)=0$ takning integration with respect to x , since $y=y(x)$ then we have the implicit relation $4x+C=|y|^{1/4}$ applying the condition $y(0)=0$ we get 4.0+C= |y(0)|^{1/4}=0 $so$ C=0 $May 1 comment Discontinuity and riemann integrability the fractional part function is periodic with period one so$ {ax} $is periodic$ 1/a$for each 'a'. discontinuities are$ 1/n \$ for n=1,2,3,4,5....