ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Fri, 20 Sep 2013 10:17:18 +0200Working with formal power serieshttps://ask.sagemath.org/question/10553/working-with-formal-power-series/This is a simplified version of my previous [question](http://ask.sagemath.org/question/3012/integrating-formal-laurent-series).
1) Is it possible to define a formal power series in sage by giving an expression for the n-th coefficient, e.g. as the expression "n" defines the power series 0 + 1 x + 2 x^2 + 3 x^3 + ... n x^n + ... ?
2) Does sage know how to multiply such objects by convolving the terms? Can it anti-differentiate them symbolically?
anilbvFri, 20 Sep 2013 10:17:18 +0200https://ask.sagemath.org/question/10553/integrating formal Laurent serieshttps://ask.sagemath.org/question/10546/integrating-formal-laurent-series/I would like to compute some integrals of products of Laurent series, with the goal of getting an explicit expression for the n-th coefficient of the result. It gets pretty messy so I was hoping that sage could keep track of the details for me. Here are the things I don't know how to do:
1) Define a Laurent series by giving an expression for its n-th coefficient.
2) Formally multiply and integrate Laurent series, producing an explicit expression for the n-th coefficient of the result.
Is this possible? I apologize if some or all of this is explained elsewhere.
EDIT: An example of what I want to do would be to define a power series such as sum(n * x^n,n,0,infinity) and then integrate it and/or multiply it by another power series, resulting in yet another power series whose coefficients I can read off. The O(x^n) notation is not very useful to me since I would like to have an expression for an arbitrary coefficient of that resulting series in terms of n.anilbvWed, 18 Sep 2013 19:39:16 +0200https://ask.sagemath.org/question/10546/