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Question: A bug in MultiSeries?

Question:A bug in MultiSeries?

ablmf 25 Maple
series multiseries
January 16 2018
0

I am trying to use MultiSeris package to expand a function (nu3 in the code).

The function has two variables, w and u. I want Maple to treat w as a constant and u as the variable.

As you can see from the code, somehow if I replace w by any rational number and do the expansion, I get an expansion with a constant * u term. However, if I replace w with zeta(3) (or pi), then some how the u term vanishes. I think this cannot be correct. Is this a bug?
 

nu3 := -sqrt(-2*sqrt(w)*sqrt(w+2)*u^4+2*u^4*w+4*sqrt(w)*sqrt(w+2)*u^2+u^4-4*u^2*w-2*sqrt(w)*sqrt(w+2)-2*u^2+w^2+2*w+1)+sqrt(-2*sqrt(w)*sqrt(w+2)*u^4+2*u^4*w+4*sqrt(w)*sqrt(w+2)*u^2+u^4-4*u^2*w-2*sqrt(w)*sqrt(w+2)-2*u^2+2*sqrt(-2*sqrt(w)*sqrt(w+2)*u^4+2*u^4*w+4*sqrt(w)*sqrt(w+2)*u^2+u^4-4*u^2*w-2*sqrt(w)*sqrt(w+2)-2*u^2+w^2+2*w+1)+2)+w-1

-(-2*w^(1/2)*(w+2)^(1/2)*u^4+2*u^4*w+4*w^(1/2)*(w+2)^(1/2)*u^2+u^4-4*u^2*w-2*w^(1/2)*(w+2)^(1/2)-2*u^2+w^2+2*w+1)^(1/2)+(-2*w^(1/2)*(w+2)^(1/2)*u^4+2*u^4*w+4*w^(1/2)*(w+2)^(1/2)*u^2+u^4-4*u^2*w-2*w^(1/2)*(w+2)^(1/2)-2*u^2+2*(-2*w^(1/2)*(w+2)^(1/2)*u^4+2*u^4*w+4*w^(1/2)*(w+2)^(1/2)*u^2+u^4-4*u^2*w-2*w^(1/2)*(w+2)^(1/2)-2*u^2+w^2+2*w+1)^(1/2)+2)^(1/2)+w-1

 (1)

with(MultiSeries)

[AddFunction, FunctionSupported, GetFunction, LeadingTerm, RemoveFunction, SeriesInfo, asympt, limit, multiseries, series, taylor]

 (2)

series(subs(w = 7/13, nu3), u = 0, 3)

series((-(-(2/13)*7^(1/2)*33^(1/2)+400/169)^(1/2)-6/13)+((1/13)*26^(1/2)*((2*7^(1/2)*33^(1/2)*(-(2/13)*7^(1/2)*33^(1/2)+400/169)^(1/2)+2*7^(1/2)*33^(1/2)-27*(-(2/13)*7^(1/2)*33^(1/2)+400/169)^(1/2)-27)/(-(2/13)*7^(1/2)*33^(1/2)+400/169)^(1/2))^(1/2))*u-((1/13)*(2*7^(1/2)*33^(1/2)-27)/(-(2/13)*7^(1/2)*33^(1/2)+400/169)^(1/2))*u^2+O(u^3),u,3)

 (3)

series(subs(w = 1, nu3), u = 0, 3)

series(-(-2*3^(1/2)+4)^(1/2)+(2^(1/2)*((2*3^(1/2)*(-2*3^(1/2)+4)^(1/2)+2*3^(1/2)-3*(-2*3^(1/2)+4)^(1/2)-3)/(-2*3^(1/2)+4)^(1/2))^(1/2))*u-((-3+2*3^(1/2))/(-2*3^(1/2)+4)^(1/2))*u^2+O(u^3),u,3)

 (4)

series(subs(w = zeta(3), nu3), u = 0, 2)

series((-(-2*zeta(3)^(1/2)*(zeta(3)+2)^(1/2)+zeta(3)^2+2*zeta(3)+1)^(1/2)+(-2*zeta(3)^(1/2)*(zeta(3)+2)^(1/2)+2*(-2*zeta(3)^(1/2)*(zeta(3)+2)^(1/2)+zeta(3)^2+2*zeta(3)+1)^(1/2)+2)^(1/2)+zeta(3)-1)-((2*(-2*zeta(3)^(1/2)*(zeta(3)+2)^(1/2)+2*(-2*zeta(3)^(1/2)*(zeta(3)+2)^(1/2)+zeta(3)^2+2*zeta(3)+1)^(1/2)+2)^(1/2)*zeta(3)^(1/2)*(zeta(3)+2)^(1/2)-2*zeta(3)^(1/2)*(zeta(3)+2)^(1/2)*(-2*zeta(3)^(1/2)*(zeta(3)+2)^(1/2)+zeta(3)^2+2*zeta(3)+1)^(1/2)-2*(-2*zeta(3)^(1/2)*(zeta(3)+2)^(1/2)+2*(-2*zeta(3)^(1/2)*(zeta(3)+2)^(1/2)+zeta(3)^2+2*zeta(3)+1)^(1/2)+2)^(1/2)*zeta(3)+2*zeta(3)*(-2*zeta(3)^(1/2)*(zeta(3)+2)^(1/2)+zeta(3)^2+2*zeta(3)+1)^(1/2)-2*zeta(3)^(1/2)*(zeta(3)+2)^(1/2)-(-2*zeta(3)^(1/2)*(zeta(3)+2)^(1/2)+2*(-2*zeta(3)^(1/2)*(zeta(3)+2)^(1/2)+zeta(3)^2+2*zeta(3)+1)^(1/2)+2)^(1/2)+(-2*zeta(3)^(1/2)*(zeta(3)+2)^(1/2)+zeta(3)^2+2*zeta(3)+1)^(1/2)+2*zeta(3)+1)/((-2*zeta(3)^(1/2)*(zeta(3)+2)^(1/2)+2*(-2*zeta(3)^(1/2)*(zeta(3)+2)^(1/2)+zeta(3)^2+2*zeta(3)+1)^(1/2)+2)^(1/2)*(-2*zeta(3)^(1/2)*(zeta(3)+2)^(1/2)+zeta(3)^2+2*zeta(3)+1)^(1/2)))*u^2+O(u^4),u,4)

 (5)

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