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Question: representing infinite series in sigma form

Question:representing infinite series in sigma form

one pound 35 Maple
gfun series
May 20 2018
0

I'm  trying to converting an infinite series from several terms to sigma form.

The series in question is:

x-x^2/(t*Log[t])+(2/3)*x^3/(t^2*Log[t]^2)+(-1/(2*t^3*Log[t]^3)-1/(4*t^3*Log[t]^2)-1/(6*t^3*Log[t]))*x^4+(2/(5*t^4*Log[t]^4)+2/(5*t^4*Log[t]^3)+4/(15*t^4*Log[t]^2))*x^5+(-1/(3*t^5*Log[t]^5)-1/(2*t^5*Log[t]^4)-5/(12*t^5*Log[t]^3)-5/(36*t^5*Log[t]^2)-1/(15*t^5*Log[t]))*x^6+(2/(7*t^6*Log[t]^6)+4/(7*t^6*Log[t]^5)+25/(42*t^6*Log[t]^4)+1/(3*t^6*Log[t]^3)+46/(315*t^6*Log[t]^2))*x^7+(-1/(4*t^7*Log[t]^7)-5/(8*t^7*Log[t]^6)-19/(24*t^7*Log[t]^5)-19/(32*t^7*Log[t]^4)-19/(60*t^7*Log[t]^3)-7/(80*t^7*Log[t]^2)-1/(28*t^7*Log[t]))*x^8+(2/(9*t^8*Log[t]^8)+2/(3*t^8*Log[t]^7)+1/(t^8*Log[t]^6)+25/(27*t^8*Log[t]^5)+163/(270*t^8*Log[t]^4)+106/(405*t^8*Log[t]^3)+88/(945*t^8*Log[t]^2))*x^9+(-1/(5*t^9*Log[t]^9)-7/(10*t^9*Log[t]^8)-73/(60*t^9*Log[t]^7)-4/(3*t^9*Log[t]^6)-149/(144*t^9*Log[t]^5)-691/(1200*t^9*Log[t]^4)-18569/(75600*t^9*Log[t]^3)-761/(12600*t^9*Log[t]^2)-1/(45*t^9*Log[t]))*x^10I've attached the worksheet 1.mw.

The example below works but not for the above I just get:

Error, invalid arguments to coeffs

Not sure where I'm going wrong any idea how to do this?

EXAMPLE that works from https://math.stackexchange.com/questions/2786296/strategy-or-software-for-representing-infinite-series-in-sigma-form

I've also attached the worksheet for this 2.mw

=>

S:= 1-x+4/3*(x^2)-2*x^3+16/5*(x^4)-16/3*(x^5)+64/7*(x^6)-16*x^7+256/9*(x^8)-256/5*(x^9)+1024/11*(x^10);

Coeffs:= [seq(coeff(S, x, j), j=0..10)];

g:= gfun:-guessgf(Coeffs,x);

convert(g[1], FPS, x);

results in:

Sum((-1)^k*2^k*x^k/(k+1), k = 0 .. infinity)

or 

rec:= gfun:-listtorec(Coeffs, a(n));

aa:= rsolve(rec[1],a(n));

Sum(aa*x^n, n=0..infinity);

results in the same desired result.

 
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