2016-11-29 04:47:21 -0500 received badge ● Nice Question (source) 2014-06-29 13:33:12 -0500 received badge ● Popular Question (source) 2014-06-29 13:33:12 -0500 received badge ● Notable Question (source) 2014-06-29 13:33:12 -0500 received badge ● Famous Question (source) 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). 2012-02-17 15:30:22 -0500 received badge ● Student (source) 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: R10 = QQ['a0,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10'] a0,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10 = R10.gens() R. = PowerSeriesRing(R10) y = a0 + a1*x + a2*x^2 + a3*x^3 + a4*x^4 + a5*x^5 + \ a6*x^6 + a7*x^7 + a8*x^8 + a9*x^9 + a10*x^10 + O(x^11) y1 = y.derivative() y2 = y1.derivative() y3 = y2.derivative() y4 = y3.derivative() f = (1+x)*y4-y1*y2 i = ideal(f) # g = i.groebner_fan(); g.reduced_groebner_bases() # a wish # q = R.quotient(i) # works, but not so useful by itself  and my other approaches ended in tracebacks: x = var('x'); y = function('y', x) desolve(diff(y,x,4)-diff(y,x)*diff(y,x,2)/(1 + x), y, contrib_ode=True) # NotImplementedError: Maxima was unable to solve this ODE. desolve_laplace(diff(y,x,4) - diff(y,x)*diff(y,x,2)/(1 + x), y) # TypeError: unable to make sense of Maxima expression  I would like to at least solve that and determine the radius of convergence. Ideally (more generally), it would be nice to have a good bag of tricks for working with series DEs such as I imagine others have already created. For this, I would like to find or develop techniques to incorporate: 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.