fredrik-j.blogspot.com
Fredrik Johansson: Euler-Maclaurin summation of hypergeometric series
http://fredrik-j.blogspot.com/2010/07/euler-maclaurin-summation-of.html
Wednesday, July 28, 2010. Euler-Maclaurin summation of hypergeometric series. I recently fixed another corner case (it's always the corner cases that are hard! In the hypergeometric function evaluation code in mpmath. The difficulty in question concerns the functions. Of which the Gauss hypergeometric function. Is an important special case. These functions can be thought of as generalizations of the geometric series. And the natural logarithm. Numerical evaluation is fairly easy for z. Which is extremely...
fredrik-j.blogspot.com
Fredrik Johansson: Assorted special functions update
http://fredrik-j.blogspot.com/2010/06/assorted-special-functions-update.html
Tuesday, June 15, 2010. Assorted special functions update. Over the week-and-a-half since the last blog update, I've gotten a bunch more work done on special functions in mpmath. Function plots in the documentation. I have started adding graphics of special functions to the documentation. So far, I've done most of the Bessel-type functions. Many more to come! Example screenshot (see the Bessel functions page):. New inhomogeneous Bessel functions. With some specific right-hand side g. I have rewritten the...
fredrik-j.blogspot.com
Fredrik Johansson: Incomplete elliptic integrals complete
http://fredrik-j.blogspot.com/2010/06/incomplete-elliptic-integrals-complete.html
Monday, June 21, 2010. Incomplete elliptic integrals complete. I'm very happy to finally have implemented incomplete elliptic integrals in mpmath (they were probably the most-requested missing special functions). Now mpmath can compute the three classical (Legendre) elliptic integrals. As well Carlson's symmetric integrals. Previously only the complete integrals K. The functions are called, respectively,. Although this could change before the release. For the code, see r1162. And height 2 b. Switched, wh...
fredrik-j.blogspot.com
Fredrik Johansson: March 2011
http://fredrik-j.blogspot.com/2011_03_01_archive.html
Monday, March 14, 2011. 100 mpmath one-liners for pi. Since it's pi day today, I thought I'd share a list of mpmath one-liners for computing the value of pi to high precision using various representations in terms of special functions, infinite series, integrals, etc. Most of them can already be found as doctest examples in some form in the mpmath documentation. A few of the formulas explicitly involve pi. Using those to calculate pi is rather circular. From mpmath import *. Chop(2*j*log( 1-j)/(1 j) ).
mabshoff.blogspot.com
Adventures in Open Source Math: December 2007
http://mabshoff.blogspot.com/2007_12_01_archive.html
Adventures in Open Source Math. Saturday, December 29, 2007. The Sorry State of Dynamic Libraries on Cygwin. This is a follow up to my previous post on the Cygwin port of Sage 2.9.1.1. What started initially about some linking issue with libpari resolved itself into a very unexpected way: libpari.dll ended up in $PREFIX/bin instead of $PREFIX/lib. After I found the DLL by accident I discovered even more bizar behavior specific to Cygwin:. Most do not create proper def files for imports. They put them int...
mabshoff.blogspot.com
Adventures in Open Source Math: February 2008
http://mabshoff.blogspot.com/2008_02_01_archive.html
Adventures in Open Source Math. Tuesday, February 26, 2008. Some times I am right, often I am wrong. Oh well, Ondrej Certik. Offered a debugging challenge. In Sage he discovered. The problem was that he hit a timeout when starting up a binary copy of Sage on his shiny, new and fast Intel Quad Code box. After some debugging he discovered that Debian's XFS default mount options cause the slowdown, all the details can be found in this blog entry. Saturday, February 23, 2008. Sage 2.10.2. Oh well, Sage Days 7.
fredrik-j.blogspot.com
Fredrik Johansson: March 2010
http://fredrik-j.blogspot.com/2010_03_01_archive.html
Wednesday, March 17, 2010. The generalized hypergeometric function. Can itself be generalized endlessly. I have recently implemented three such extensions in mpmath: bilateral series, two-dimensional hypergeometric series, and q. Analog (or "basic") hypergeometric series. The bilateral hypergeometric series. Is the simplest extension, and consists of taking the usual hypergeometric series and extending the range of summation from [0,∞) to (-∞,∞):. This series only converges when z. From mpmath import *.
fredrik-j.blogspot.com
Fredrik Johansson: Move along
http://fredrik-j.blogspot.com/2012/01/move-along.html
Thursday, January 26, 2012. I'm moving my blog to http:/ fredrikj.net/blog. If you're living in the future and reading this, you should go there instead! Thursday, January 26, 2012. This comment has been removed by a blog administrator. July 22, 2013 at 10:48 AM. Subscribe to: Post Comments (Atom). This blog is mostly about my work on free software projects, including mpmath. Since 2010, I'm a PhD student in the Algorithmic Combinatorics group at RISC. View my complete profile.
fredrik-j.blogspot.com
Fredrik Johansson: September 2010
http://fredrik-j.blogspot.com/2010_09_01_archive.html
Friday, September 24, 2010. Announcing mpmath 0.16. I'm happy to announce the release of mpmath 0.16. Which contains the usual bugfixes as well as a slew of new features! The main focus has been to improve coverage of special functions. Additions include inhomogeneous Bessel functions, Bessel function zeros, incomplete elliptic integrals, and parabolic cylinder functions. As of 0.16, mpmath implements essentially everything listed in the NIST Digital Library of Mathematical Functions. For computation of ...
fredrik-j.blogspot.com
Fredrik Johansson: Some FLINT 2.2 highlights
http://fredrik-j.blogspot.com/2011/06/some-flint-22-highlights.html
Wednesday, June 8, 2011. Some FLINT 2.2 highlights. Version 2.2 of FLINT. Fast Library for Number Theory) was released. Last weekend. Some updated benchmarks. In this blog post, I'm going to talk a bit about features I contributed in this version. With apologies to Sebastian Pancratz. Who wrote a whole lot of code as well - in particular, a new module for computing with p-adic numbers, and a module for rational functions! I've added various functions for polynomial interpolation to the fmpz poly. There a...
