MaplePrimes - answers and comments on Question, expressing function with series

Errors?

Scott03 — Tue, 18 May 2010 20:08:27 Z

Could you let us know what you tried to execute to do this and what errors did you get?

Are you looking for something like the following:

eq1:=v*t = S0-S[t]+Km*ln(S0/S[t]);
eq2:=isolate(eq1, S[t]);
seq(eval(rhs(eq2), t = t), t = 1 .. 5);

Scott

I got St function and want

lomkes — Tue, 18 May 2010 21:13:04 Z

I got S_t function and want to express it in row(ex. taylor maybe) how do I do it??

Taylor

hirnyk — Wed, 19 May 2010 21:18:05 Z

Maybe, Taylor expansion is that you want. The command >series produces the same result. It is useful to evaluate the parameters v, S0, Km, e. The outputs are too large to be cited here.

> St := LambertW((S0*e-(v*t-S0)/Km*(1/Km))*Km);

>T:= taylor(St, t = 0,10); S:=series(St, t = 0,10);

You might convert these expansions to polynomials, getting rid of Os (T cannot be evaluated at t, TP can):

>TP:=convert(T,polynom); SP:=convert(S,polynom);

S0:=1; Km:=11; v:=1; I put

lomkes — Wed, 19 May 2010 23:16:50 Z

S0:=1; Km:=11; v:=1; I put those and I get simplified smaller outputs, but don't know how to post them here. Anyway another questions. 1) How do I calc that taylor expansion?? t=5 as an example 2) Is there any chance to plot it? 3) how do I plot unexpressed S[t] function?

mtaylor

alec — Wed, 19 May 2010 23:53:35 Z

That also could be done with mtaylor which produces polynomials instead of series,

S0:=1: Km:=11: v:=1:
sol:=solve(v*t=(S0-St)+Km*ln(S0/St),St):
eval(sol,t=5.);

                             0.6549618124

plot(sol);

s:=unapply(mtaylor(sol,t),t);

                          11   2     11    3      143     4
  s := t -> 1 - 1/12 t + ---- t  - ------ t  + --------- t
                         3456      165888      286654464

               2629      5
         + ------------ t
           206391214080

s(5.);

                             0.6549679603

plot(s);

Alec

are you asking the right question here?

Axel Vogt — Thu, 20 May 2010 00:00:00 Z

I do not understand all of your words (like "row" ...)

But it is my impression you want values and do not like the answer 'LambertW'.

If it is so then however it is (in general) not the right way to ask for a Taylor series ...
and you should not hesitate to ask your actual question.

Sorry, if that is a wrong impression.

PS: that is an example, why it makes sense to provide a more complete profile,
often it is just the language (certainly in my case) or interest which may hint
others to give you an adequate reply