MaplePrimes - answers and comments on Question, How to extract coefficient from Probability Generating function

floating-point

Pseudomodo — Wed, 04 Jul 2012 18:50:26 Z

Have you tried using evalf(Sum(....,k=1..infinity)) instead of sum(....,k=1..infinity) ?

By surgery

Markiyan Hirnyk — Wed, 04 Jul 2012 22:02:13 Z

You ask:"`HERE I NEED HELP, because I need to copy and paste the expression of a(k), c(k).`
Question : Is there any way to extract the coefficients of z`^(k)?`
So that I can avoid the copy pasting?"
It can be done by surgery:
> B := convert(B(z), FormalPowerSeries, z);

> op([1, 1], B);

convert(B(z),FormalPowerSeries,z) not working for fraction value

dj_gssst — Mon, 13 Aug 2012 22:11:49 Z

Dear Experts,

I went for Vacation. Many many thanks for your timely help, finally I am able to find out the k-th co-efficient of z^k. Now I have similar problem for fraction values inside B(z) function. I am unable to get the output of convert(B(z),FormalPowerSeries,z) function as summation and hence unable to find the k-th co-efficient using op[1,1]. I have attached the Maple file. Please help me.Quest_FormalPower_Co.mw

Correction

Markiyan Hirnyk — Mon, 13 Aug 2012 23:12:16 Z

Here is your corrected code, which works.

>restart;
>lambda := 1.0: mu := 1.2: eta := 1.4: xi := .6:

> B := proc (z) options operator, arrow; lambda^2/(lambda+xi+eta-eta*z)^2 end proc; B(z);

> Y := convert(convert(B(z), rational), FormalPowerSeries, z);#pay attention to convert,rational command

> temp := op([1, 1], Y);#in your code temp := op([1, nops(Y)], Y)

> b := unapply(temp, k);

corrected_code.mw

summation upto infinity worked

dj_gssst — Thu, 05 Jul 2012 21:43:25 Z

Dear experts,

evalf(Sum(..,k=0..infinity)); worked fine. But the same function doesn't work if the summand variable is a solution of two equations. I have given the code

Download Quest_FormalPowerSe.mw

Point in rhs

Markiyan Hirnyk — Thu, 05 Jul 2012 22:31:30 Z

This works:
>p[1] := n-> rhs(s)*delta^(n-1);
>p[0] := n ->rhs(t)*theta^n;
>evalf(Sum(p[1](n), n = 1 .. 100))+evalf(Sum(p[0](n), n = 0 .. 100));
0.99999999999999999999999999999999999999999999999999999999999999999999/
99999999999999999999999588044159
>u := evalf(Sum(delta^(n-1)*rhs(sol[1]), n = 1 .. infinity));
u := 0.182972129718492054531369315533629828458690017655530945303012757/
1282864432650325974441103854393152750e-2
>v := evalf(Sum(theta^n*rhs(t), n = 0 .. infinity));
v := .99817027870281507945468630684466370171541309982344469054696987242/
87171355673496740255588961456068473
>u+v;
1.000000000000000000000000000000000000000000000000000000000000000000000/
000000000000000000000000000000

Why don't you apply my suggestion concerning surgery?

modified.mw