There was some paper about computing limits with oscillating functions. Maybe you can find the reference if you search the mailing list archives (or probably Raoul will remember it).
Aaron Meurer On Mon, Feb 24, 2014 at 6:27 AM, Avichal Dayal <[email protected]> wrote: > There are only two weeks before student application portal opens > and I would like to discuss my ideas regarding "Series expansion" project. > > Here is what SymPy currently does:- > series:- > 1) General expansion with O term appended > 2) No separate functions for taylor, laurent, asymptotic etc. > 3) Cannot provide a generating function or an infinite series representation > 4) Bugs when expansion point is other than zero > > For 3) we need to implement Formal Power Series > Formal Power Series: > Other CAS like Maple, Mathematica have this functionality and we must > also have it. > This has two parts: > 1) Give a formula or sequence and get the infinite series > 2) Give a function and get the infinite series > Once we get the infinite series, we can do various operations on it. > > Main points: > 1) Representation of infinite sum. Is there a way to represent summation > yet in SymPy? > 2) Implement algorithm that can create a generating function given an > expression. > This paper gives such an algorithm: > http://www.mathematik.uni-kassel.de/~koepf/Publikationen/SC-93-31.pdf > It uses recurrence relations and differential equations to do so. > I'm currently going through it > and understanding it. > > Asymptotic Expansion: > Many special and elementary functions do not have it implemented. I plan > to do > it for all whose expansion is possible. > > In general also SymPy does not do it properly. > For e.g.:- > series(sin(1/x+exp(-x))-sin(1/x), x, oo, 2) currently gives > O(1/x**2) > It can be better expanded as:- > 1/exp(x) - 1/(2*exp(x)*x**2) + O(1/(exp(x)*x**4)) > > The following paper gives an algorithm to find such an asymptotic > expansion: > A new algorithm for computing asymptotic series by "Dominik Gruntz" > > Main points: > 1) When to do an asymptotic expansion? > Currently, series just replaces x->1/x and oo->0 and does normal > series expansion on the project. > > Order Term arithmetic: > This PR by @skirpichev currently deals with it: > https://github.com/sympy/sympy/pull/2427 > I'll be more than happy to work on it and extend it. > > Please reply to give your opinion. Thank You! > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sympy. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/af766c64-f73e-46aa-8b00-393fb9ca82ac%40googlegroups.com. > For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAKgW%3D6JU1NUYAHcow8oS%2B3JV_9_9x7vDXtUdt-c%3D3MXTUguY7g%40mail.gmail.com. For more options, visit https://groups.google.com/groups/opt_out.
