Posted in Linux, Mathematics, Physics, Science, tagged Calculation, chromium, CLI, Command, Expansion, Free, Google, Group, Groups, How to, HowTo, Linux, Maple, Mathematica, Mathematics, Matlab, Notebook, Online, Packages, Programming, Python, Sage, Sage-dev, Sagemath, Series, Symbolic, Taylor, Terminal, Tips and Tricks, Ubuntu, Web Browser on February 19, 2011|
Leave a Comment »

Two days ago I was trying to expand in series a lot of functions… so I ask myself, Could it be done in SAGE? It should be possible… but, How? ðŸ˜›

So I ask on google group.

#### Solution by Andrzej Chrzeszczyk

sage: var('r');
sage: f=2*r/sinh(2*r)
sage: f.taylor(r,0,5)
14/45*r^4 - 2/3*r^2 + 1
sage: maxima(f).powerseries('r',0)
-4*r*'sum((2^(2*i2-1)-1)*2^(2*i2-1)*bern(2*i2)*r^(2*i2-1)/
(2*i2)!,i2,0,inf)

This solution uses a power series expansion from maxima… really nice feature! Isn’t it?

Ah… and this expansion is around .

If one would like the asymptotic expansion ,

sage: maxima(f).powerseries('r',infinity)
-4*r*'sum((2^(2*i3-1)-1)*2^(2*i3-1)*bern(2*i3)*r^(2*i3-1)/
(2*i3)!,i3,0,inf)

However, note that this expansion coincides with the previous one, i.e., it’s the function itself. It couldn’t be that perfect. ðŸ˜‰

#### Solution by Francois Maltey

Use the *Taylor* command of SAGE,

Around zero
sage: taylor (2*x/sinh(2*x), x, 0, 10)
-292/13365*x^10 + 254/4725*x^8 - 124/945*x^6 + 14/45*x^4 - 2/3*x^2 + 1

Around infinity… a trick! change and expand around zero ðŸ™‚
sage: taylor (2*1/x/((exp(2/x)-exp(-2/x))/2), x, 0, 12)
4*e^(-10/x)/x + 4*e^(-6/x)/x + 4*e^(-2/x)/x

Thank you guys!

Enjoy!

Dox

51.609574
-3.980685

Read Full Post »