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Question: what does this result from Maple mean?

Question:what does this result from Maple mean?

jrive 195 Maple 2023
rootof summation
October 08 2024
0

I do not understandwhat this result from Maple means.

I don't know what it means when a result has "Root of", and in this case, there is also a big summation sign for which I can't tell if the variables underneath it are part of the summartion, or what.  I'd appreciate any guidance to make sense of what this means..

restart

with(inttrans)

assump := R1::real, R2::real, L1::real, C1::real, C2::real, L2::real, omega::real, M::real, R1 > 0, R2 > 0, L1 > 0, C1 > 0, L2 > 0, C2 > 0, omega > 0, M > 0

R1::real, R2::real, L1::real, C1::real, C2::real, L2::real, omega::real, M::real, 0 < R1, 0 < R2, 0 < L1, 0 < C1, 0 < L2, 0 < C2, 0 < omega, 0 < M

 (1)

expr := Vin/(s*(R1+s*L1-1/(s*C1)+(omega*M)^2/(R2+s*L2-1/(s*C2))))

Vin/(s*(R1+s*L1-1/(s*C1)+omega^2*M^2/(R2+s*L2-1/(s*C2))))

 (2)

invlaplace(expr, s, t)

Vin*C1*(sum(exp(_alpha*t)*(-1+C2*_alpha*(L2*_alpha+R2))/(4*C1*C2*L1*L2*_alpha^3+2*C1*C2*M^2*_alpha*omega^2+3*C1*C2*L1*R2*_alpha^2+3*C1*C2*L2*R1*_alpha^2+2*C1*C2*R1*R2*_alpha-2*C1*L1*_alpha-2*C2*L2*_alpha-C1*R1-C2*R2), _alpha = RootOf(1+C1*C2*L1*L2*_Z^4+(C1*C2*L1*R2+C1*C2*L2*R1)*_Z^3+(C1*C2*M^2*omega^2+C1*C2*R1*R2-C1*L1-C2*L2)*_Z^2+(-C1*R1-C2*R2)*_Z)))

 (3)

NULL

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