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2012-05-08 10:55:22 -0500 | commented question | How to calculate $L'(1,\chi)/L(1,\chi)$? Have you had a look at the [L-function tutorial](http://wiki.sagemath.org/days33/lfunction/tutorial) from Sage days 33? In particular, it has some fairly recent comments on the development status. I have no idea whether Sage yet implements, for example, the insights in Ihara, Murty & Shimura's paper from circa 2007, [On the Logarithmic Derivative of Dirichlet L-Functions at s=1](http://www.kurims.kyoto-u.ac.jp/~kenkyubu/emeritus/ihara/Publications-and-Recent-Preprints/RecentArticles/pdf-files/IMS.main.pdf). |

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2012-02-15 01:33:26 -0500 | asked a question | series solutions of higher order ODEs I'm trying to use Sage to find the general series solution to $y^{(4)}=\frac{y'y''}{1+x}$. So far my best efforts to derive the coefficient recurrence relations, inspired by a good book draft, have been along these lines: and my other approaches ended in tracebacks: I would like to at least solve that and determine the radius of convergence. - more convenient coefficients, e.g. from this thread
- a way to derive the recurrence relations using Python's lambda operator or this nice trick
- a solver for higher order ODEs such as above
Any hints, links, references or suggestions would be appreciated. |

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