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| bio | website | tpfto.wordpress.com |
|---|---|---|
| location | Kalakhang Maynila | |
| age | ||
| visits | member for | 2 years, 10 months |
| seen | 47 mins ago | |
| stats | profile views | 11,093 |
Some know it all, while some act dumb.
Let the bass line strum to the bang of the drum.
Some can swim, while some will sink;
and some will find their minds and think
— Kiko Magalona, Kaleidoscope World
This place sure is becoming less enjoyable by the day... \ If you believe there is a question on the main site that absolutely needs my eyes/expertise(?), try pinging me in the chatroom.
"Math doesn't suck, you do" by Maddox
Any code I've posted here I place under the WTFPL.
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1d |
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How to solve $\int_0^\infty J_0(x)\ \text{sinc}(\pi\,x)\ e^{-x}\,\mathrm dx$? @Zakharia, you did notice the word "almost", no? ;) |
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May 19 |
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A matrix w/integer eigenvalues and trigonometric identity Have you seen this article, by any chance? |
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May 19 |
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What is $-i$ exactly? If you take moving along the usual number line as moving forward of backward, depending on the sign, and then extend this analogy to the complex plane, you could think of $\pm i$ as going either left or right, depending on your choice of convention. |
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May 19 |
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Why does Newton's method work? @Ross, I'll see if I can redo the images later; I lost the code for generating them... anyway, the idea I had with the coloring is to denote the previous approximation with a lighter hue than the current one, as if leaving a "shadow". |
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May 18 |
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Can't argue with success? Looking for “bad math” that “gets away with it” @kjo, I had this in mind. Search that site for other issues, all featuring Lucky Larry. (For some reason that message did not ping me; I only came upon this thread again by accident.) |
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May 18 |
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Prove every odd integer is the difference of two squares @Eric, I seem to recall an answer of yours that also does this... :) |
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May 18 |
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How to integrate e to the power to the power? @Sharkos, see this. |
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May 16 |
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Integral of product of Bessel functions of the first kind Gradshteyn/Ryzhik ought to have this as well... |
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May 15 |
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What type of Hypergeometric series is this? From a quick glance, it doesn't look like any of the Horn functions... |
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May 15 |
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(fractional) half derivative of $ {1 \over 1-x }$? +1; your last bit is one of the good ways to check a semiderivative; semidifferentiating a function twice should certainly yield the function's usual first derivative. |
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May 14 |
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Why is a full turn of the circle 360°? Why not any other number? @Lubin, well, they're weird. ;) (FWIW, I'd almost always use degrees when I'm not talking to someone with scientific sophistication, e.g. carpenters.) |
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May 14 |
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Why is a full turn of the circle 360°? Why not any other number? You mean the mil? A very convenient unit, especially for sniping purposes... |
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May 14 |
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Can someone please explain $e$ in layman's term? @Hagen, I prefer writing $\exp(x)$ too, but I thought introducing that notation is best left to a nicely expository answer... |
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May 14 |
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Can someone please explain $e$ in layman's term? I would say you should be more interested in the function $e^x$ than the constant $e$... |
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May 14 |
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How to verify the order of DOPRI Runge-Kutta method Have you seen the discussion in Hairer/Nørsett/Wanner? In particular, they explain there why they've elected to use a 5th order and a 3rd order embedded RK method along with the Dormand-Prince coefficients for error estimation purposes, instead of the seventh-order method. |
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May 13 |
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Continued fraction expansion related to exponential generating function As I've seen, you're currently looking at Viscovatov's algorithm. I'm thinking another approach you might want to pursue is Thiele expansion of the Debye function; basically, the CF analog of Taylor expansion, which uses the "reciprocal derivative" instead of the derivative in Taylor's expansion. There should be literature on this... |
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May 13 |
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Who was V. Viskovatov? There's also a nice discussion of Viscovatov's algorithm in Lorentzen/Waadeland's Continued Fractions with Applications and Cuyt/Wuytack's Nonlinear Methods in Numerical Analysis. Is this related to your quest to determine a CF expansion of the polylogarithm? |
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May 13 |
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Factorial of infinity A related question. |
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May 13 |
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Factorial of infinity I suppose one could be charitable and say that the result in the OP is the Dirichlet regularization of the factorial. In related news, the "product" of the prime numbers is $4\pi^2$. |
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May 13 |
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Are high dimensional cubic interpolation and cubic spline the same? $n$-cubic interpolation is a bit more general than spline interpolation; in the former, you get to additionally prescribe (partial) derivative values; cubic splines, while they also use derivatives, go one step further and prescribe that the resulting interpolant is not only continuous, but also differentiable (up to a certain point). |
