User - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T10:22:15Z http://mathoverflow.net/feeds/user/23964 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/126850/gram-series-for-more-general-integrals Gram series for more general integrals unknown (yahoo) 2013-04-08T13:06:27Z 2013-04-08T13:06:27Z <p>given the Gram series</p> <p>$$\pi (x) \sim \sum_{n=1}^{\infty} \frac{1}{n}\frac{log^{n}(x)}{n!\zeta (n+1)}$$</p> <p>can this result be generalized to more integral transforms ?</p> <p>$$g(x)= \int_{0}^{\infty}dyK(xy)f(y)dy$$</p> <p>for exapmle in Gramm series for the prime counting function the integral equation is</p> <p>$$log\zeta(s)= s\int_{0}^{\infty}\frac{1}{e^{xy}-1}\pi(e^{y})dy$$</p> http://mathoverflow.net/questions/126839/numerical-evaluation-of-a-triple-integral-can-be-made Numerical evaluation of a triple integral can be made ? unknown (yahoo) 2013-04-08T11:14:56Z 2013-04-08T11:14:56Z <p>let be the integral</p> <p>$$\int_{0}^{\infty}dx\int_{0}^{\infty}dy\int_{0}^{\infty}dz \frac{f(x,y,z)}{(1+x^{2}+y^{2}+z^{2})^{s}}$$</p> <p>here $s$ is a parameter so the integral converges</p> <p>now let us make the change to polar coordinates , however the function $f(x,y,z)$ will not be invariant under rotations so there will be an extra integration over the angular variables</p> <p>$$\int_{\Omega} d \Omega \int_{0}^{\infty}r^{2}f(r, \Omega )(1+r^{2})^{-s}$$</p> <p>my question is can we ALWAYS integrate with Numerical (MOnte carlo method) inside the angular variables $\int_{\Omega}d \Omega$ so we are left only with a sum of one dimensional integrals ??</p> <p>$$\sum_{i} \int_{0}^{\infty}dr f(r, \Omega _{i})r^{2}(1+r^{2})^{-s}.$$</p> http://mathoverflow.net/questions/116690/bessel-function-with-complex-argument-and-index Bessel function with complex argument and index unknown (yahoo) 2012-12-18T10:03:32Z 2012-12-18T10:03:32Z <p>let be a Bessel function $J_{u} (x)$</p> <p>if both the index 'u' and the argument 'x' are complex</p> <p>$$J_{ia}(ib)$$</p> <p>for real 'a' and 'b' what is then the name for this function ??</p> <p>if only the index is complex $J_{ia}(b)$ or the argumentis complex $J_{a}(ib)$</p> <p>what is the name of this function ??</p> http://mathoverflow.net/questions/103926/how-can-i-solve-a-boundary-value-numerically-on-an-infinite-interval how can i solve a boundary value numerically on an infinite interval ?? unknown (yahoo) 2012-08-04T09:36:31Z 2012-08-05T21:08:08Z <p>let be the differential equation $-y''(x)+x^{4}y(x)-E_{n}y(x)=0$ with the boundary conditions $y(0)=0=y(\infty)$</p> <p>how could i use the shooting method or other numerical method to solve this equation ? , my only idea is to set $R=10000$ for example and solve $y(0)=0=y(R)$</p> <p>of course i also could made the substitution $u= \frac{x}{x-1}$ so the new boundary conditions could become $y(0)=0=y(1)$ but know the differential equation would be singular at the point $u=1$</p> http://mathoverflow.net/questions/127122/taylor-series-in-lgox-for-the-square-root Comment by 2013-04-11T11:37:13Z 2013-04-11T11:37:13Z oh sorry tehn Ben if possible erase teh questio please :) http://mathoverflow.net/questions/126839/numerical-evaluation-of-a-triple-integral-can-be-made Comment by 2013-04-10T11:00:13Z 2013-04-10T11:00:13Z my idea is to change to polar coordinates :) and then to apply numerical integration ONLY to the angular variables so we are left with a set of ONE dimensional integral in the form $\int_{0}^{\infty}drr^{n-1}f(r, \Omega _{i} )$ http://mathoverflow.net/questions/126839/numerical-evaluation-of-a-triple-integral-can-be-made Comment by 2013-04-08T19:01:55Z 2013-04-08T19:01:55Z my question was about if my numerical method is correct a) change to polar coordinates b) numerical integration ONLY over the angular variables. http://mathoverflow.net/questions/120017/why-mathematicians-do-not-accept-the-wu-sprung-semiclassical-model-as-a-solution Comment by 2013-01-27T13:47:03Z 2013-01-27T13:47:03Z <a href="http://mathdl.maa.org/images/upload_library/22/Ford/JosephKeller.pdf" rel="nofollow">mathdl.maa.org/images/upload_library/22/Ford/&hellip;</a> inverse problems in physics.. see form equation (6.1) we can get the inverse of the potentia $f^{-1}(x)$ from the eigenvalue staircase in this case the staricase is the Riemann zeta function http://mathoverflow.net/questions/120017/why-mathematicians-do-not-accept-the-wu-sprung-semiclassical-model-as-a-solution Comment by 2013-01-27T13:41:02Z 2013-01-27T13:41:02Z Hua Wu and D. W. L. Sprung, &quot;Riemann zeta and a fractal potential&quot;, Physical Review E 48 (1993) 2595. Fractal fits to Riemann zeros P B Slater, Canadian Journal of Physics, 2007, 85(4): 345–357, 10.1139/p07-050 http://mathoverflow.net/questions/34699/approaches-to-riemann-hypothesis-using-methods-outside-number-theory/112070#112070 Comment by 2012-11-12T13:06:15Z 2012-11-12T13:06:15Z as far as i know an operator of the form $-D^{2}+f(x)$ has only Real Eigenvalues doesn't it ? , of course as a phsyicist i could be wrong :D , look on the web WU-SPRUNG potential PHYSICS OF THE RIEMANN HYPOTHESIS and similar questions or simply use a computer to get the eigenvalues to see i am right http://mathoverflow.net/questions/34699/approaches-to-riemann-hypothesis-using-methods-outside-number-theory/112070#112070 Comment by 2012-11-11T14:48:38Z 2012-11-11T14:48:38Z the idea is that using WKB method , or semiclassical theory , look at this <a href="http://en.wikipedia.org/wiki/Old_quantum_theory" rel="nofollow">en.wikipedia.org/wiki/Old_quantum_theory</a> one could get a Hamiltonian with a density of states given by the Riemann Weil formula and whose energies are the Riemann Zeros the potential is given implicitly of course http://mathoverflow.net/questions/111809/how-to-deal-with-divergent-fourier-series Comment by 2012-11-08T16:07:33Z 2012-11-08T16:07:33Z given any 'x' positive i would like to find a method to sum the divergent series with $a=1/2$ or with a a real number on the interval $(0,1)$