​​Clear[Subscript];​​Clear[P,Q,r,f,R,l,k,k,v,λ,μ,a,b,myExp,mySum,myCoeff,myCoeffList];​​​​P[r_,n_,l_]:=Block[​​{res},​​res=Sum[Subscript[a,k]*(r^3-v)^((k+l)/3),{k,0,n}];​​Simplify[res]​​]​​​​Q[r_,n_,l_]:=Block[​​{res},​​res=Sum[Subscript[b,k]*(r^3-v)^((k+l)/3),{k,0,n}];​​Simplify[res]​​]​​​​myExp=Exp[Q[r,4,-2]];​​R[r]:=P[r,4,-2]*myExp;​​​​"the following sum ..."​​f[r]:=(1/r^2)*(r^3-v)^(2/3);​​mySum:=Simplify[r^3*((r^3-v)^(7/3))*(-r^2*f[r]^3*D[D[R[r],r],r]-2*r*D[R[r],r]+(λ+μ*r^2*f[r])*R[r])/myExp];​​Expand[mySum]​​"contains terms with (r^3-v)^(1/3)"​​​​"the polynomial related to the term (r^3-v)^(1/3) is"​​myCoeff:=Coefficient[Expand[mySum],(r^3-v)^(1/3)];​​myCoeff​​​​"the list of coefficients of this polynomial is"​​myCoeffList:=CoefficientList[myCoeff,r];​​myCoeffList​​​​"this list was evaluated with CoefficientList"​​"I am searching for a non-trivial solution of λ,μ,​
a
1
​,​SubscriptBox[\(a\), \(\(2\)\(,\)\(...\)\( \)\)]​that all coefficients of this list are zero"​​"how do I transform the result of CoefficitenList[] into a set of equations, which I can solve for example with Solve[]"​​​​
the following sum ...
contains terms with (r^3-v)^(1/3)
the polynomial related to the term (r^3-v)^(1/3) is
9
r
μ
a
0
-2
6
r
vμ
a
0
+
3
r
2
v
μ
a
0
+
9
r
λ
a
2
-2
6
r
vλ
a
2
+
3
r
2
v
λ
a
2
+
12
r
μ
a
3
-3
9
r
vμ
a
3
+3
6
r
2
v
μ
a
3
-
3
r
3
v
μ
a
3
-6
6
r
a
1
b
0
+6
3
r
v
a
1
b
0
+4
2
v
a
1
b
0
+6
9
r
a
4
b
0
-12
6
r
v
a
4
b
0
+10
3
r
2
v
a
4
b
0
-4
3
v
a
4
b
0
-4
3
r
a
0
2
b
0
-4
6
r
a
3
2
b
0
+4
3
r
v
a
3
2
b
0
-4
6
r
a
0
b
1
+4
3
r
v
a
0
b
1
+2
2
v
a
0
b
1
+2
9
r
a
3
b
1
-4
6
r
v
a
3
b
1
+4
3
r
2
v
a
3
b
1
-2
3
v
a
3
b
1
-4
6
r
a
2
b
0
b
1
+4
3
r
v
a
2
b
0
b
1
-
6
r
a
1
2
b
1
+
3
r
v
a
1
2
b
1
-
9
r
a
4
2
b
1
+2
6
r
v
a
4
2
b
1
-
3
r
2
v
a
4
2
b
1
-2
3
r
2
v
a
1
b
3
+2
3
v
a
1
b
3
-6
12
r
a
4
b
3
+18
9
r
v
a
4
b
3
-20
6
r
2
v
a
4
b
3
+10
3
r
3
v
a
4
b
3
-2
4
v
a
4
b
3
+4
6
r
a
0
b
0
b
3
-4
3
r
v
a
0
b
0
b
3
+4
9
r
a
3
b
0
b
3
-8
6
r
v
a
3
b
0
b
3
+4
3
r
2
v
a
3
b
0
b
3
+2
9
r
a
2
b
1
b
3
-4
6
r
v
a
2
b
1
b
3
+2
3
r
2
v
a
2
b
1
b
3
-
9
r
a
0
2
b
3
+2
6
r
v
a
0
2
b
3
-
3
r
2
v
a
0
2
b
3
-
12
r
a
3
2
b
3
+3
9
r
v
a
3
2
b
3
-3
6
r
2
v
a
3
2
b
3
+
3
r
3
v
a
3
2
b
3
+2
9
r
a
0
b
4
-4
6
r
v
a
0
b
4
-2
3
r
2
v
a
0
b
4
+4
3
v
a
0
b
4
-10
12
r
a
3
b
4
+30
9
r
v
a
3
b
4
-34
6
r
2
v
a
3
b
4
+18
3
r
3
v
a
3
b
4
-4
4
v
a
3
b
4
+8
9
r
a
2
b
0
b
4
-16
6
r
v
a
2
b
0
b
4
+8
3
r
2
v
a
2
b
0
b
4
+4
9
r
a
1
b
1
b
4
-8
6
r
v
a
1
b
1
b
4
+4
3
r
2
v
a
1
b
1
b
4
+4
12
r
a
4
b
1
b
4
-12
9
r
v
a
4
b
1
b
4
+12
6
r
2
v
a
4
b
1
b
4
-4
3
r
3
v
a
4
b
1
b
4
-4
12
r
a
2
b
3
b
4
+12
9
r
v
a
2
b
3
b
4
-12
6
r
2
v
a
2
b
3
b
4
+4
3
r
3
v
a
2
b
3
b
4
-4
12
r
a
1
2
b
4
+12
9
r
v
a
1
2
b
4
-12
6
r
2
v
a
1
2
b
4
+4
3
r
3
v
a
1
2
b
4
-4
15
r
a
4
2
b
4
+16
12
r
v
a
4
2
b
4
-24
9
r
2
v
a
4
2
b
4
+16
6
r
3
v
a
4
2
b
4
-4
3
r
4
v
a
4
2
b
4
the list of coefficients of this polynomial is
4
2
v
a
1
b
0
-4
3
v
a
4
b
0
+2
2
v
a
0
b
1
-2
3
v
a
3
b
1
+2
3
v
a
1
b
3
-2
4
v
a
4
b
3
+4
3
v
a
0
b
4
-4
4
v
a
3
b
4
,0,0,
2
v
μ
a
0
+
2
v
λ
a
2
-
3
v
μ
a
3
+6v
a
1
b
0
+10
2
v
a
4
b
0
-4
a
0
2
b
0
+4v
a
3
2
b
0
+4v
a
0
b
1
+4
2
v
a
3
b
1
+4v
a
2
b
0
b
1
+v
a
1
2
b
1
-
2
v
a
4
2
b
1
-2
2
v
a
1
b
3
+10
3
v
a
4
b
3
-4v
a
0
b
0
b
3
+4
2
v
a
3
b
0
b
3
+2
2
v
a
2
b
1
b
3
-
2
v
a
0
2
b
3
+
3
v
a
3
2
b
3
-2
2
v
a
0
b
4
+18
3
v
a
3
b
4
+8
2
v
a
2
b
0
b
4
+4
2
v
a
1
b
1
b
4
-4
3
v
a
4
b
1
b
4
+4
3
v
a
2
b
3
b
4
+4
3
v
a
1
2
b
4
-4
4
v
a
4
2
b
4
,0,0,-2vμ
a
0
-2vλ
a
2
+3
2
v
μ
a
3
-6
a
1
b
0
-12v
a
4
b
0
-4
a
3
2
b
0
-4
a
0
b
1
-4v
a
3
b
1
-4
a
2
b
0
b
1
-
a
1
2
b
1
+2v
a
4
2
b
1
-20
2
v
a
4
b
3
+4
a
0
b
0
b
3
-8v
a
3
b
0
b
3
-4v
a
2
b
1
b
3
+2v
a
0
2
b
3
-3
2
v
a
3
2
b
3
-4v
a
0
b
4
-34
2
v
a
3
b
4
-16v
a
2
b
0
b
4
-8v
a
1
b
1
b
4
+12
2
v
a
4
b
1
b
4
-12
2
v
a
2
b
3
b
4
-12
2
v
a
1
2
b
4
+16
3
v
a
4
2
b
4
,0,0,μ
a
0
+λ
a
2
-3vμ
a
3
+6
a
4
b
0
+2
a
3
b
1
-
a
4
2
b
1
+18v
a
4
b
3
+4
a
3
b
0
b
3
+2
a
2
b
1
b
3
-
a
0
2
b
3
+3v
a
3
2
b
3
+2
a
0
b
4
+30v
a
3
b
4
+8
a
2
b
0
b
4
+4
a
1
b
1
b
4
-12v
a
4
b
1
b
4
+12v
a
2
b
3
b
4
+12v
a
1
2
b
4
-24
2
v
a
4
2
b
4
,0,0,μ
a
3
-6
a
4
b
3
-
a
3
2
b
3
-10
a
3
b
4
+4
a
4
b
1
b
4
-4
a
2
b
3
b
4
-4
a
1
2
b
4
+16v
a
4
2
b
4
,0,0,-4
a
4
2
b
4

this list was evaluated with CoefficientList
I am searching for a non-trivial solution of λ,μ,​
a
1
​,​SubscriptBox[\(a\), \(\(2\)\(,\)\(...\)\( \)\)]​that all coefficients of this list are zero
how do I transform the result of CoefficitenList[] into a set of equations, which I can solve for example with Solve[]