By using frobenius method I find the roots of the indicial equation of a 4th order ODE to be
0, 1, 1, 2
Now, what is the form of the corresponding series solution of this equation with log terms?
I found numerically that for small d only four roots are admissible (two reals and two purely imaginary) but for large d two more complex conjugate roots appear.
There exists any analitical tools to define this critical value of d?
How many complex roots admit the following equation:
(2 z^2 + 1)^2 ((z + d)/(z - i))^1/2 - (2 z^2 - d)^2 ((z + i)/(z - d))^1/2 == 0
for 0 < d < 1, where i = (-1)^1/2.
Can I found how their number varies with d by using the argument principle?
Thanks in advance for helpfull suggestions