The problem is to determine a lower bound for the radius of convergence for the two following equations. I am able to get p(x) and q(x) for both equations, but I'm confused on how to proceed. I would like to see the problem worked out and what the lower bound is.
Centered at 1
what I believe are p(x) and q(x)
p(x) = and q(x) =
Centered at 0, and also try it centered at 1© BrainMass Inc. brainmass.com February 24, 2021, 2:16 pm ad1c9bdddf
Please see the attached doc file and please do not hesitate to contact me through the BrainMass staff if there is any vagueness. Good Luck.
and we want the lower bound for the radius of convergence about x=1. First we divide the equation by x^2:
now the radius is at least equal to the minimum between the radii of 1/x and (x^2-v)/x^2 about x=1:
1/x=1/(1+(x-1))=1-(x-1)+(x-1)^2-(x-1)^3+... provided |x-1|<1 therefore the radius of convergence about x=1 for the first one is 1.
we can ...
The expert finds the lower bounds for Bessel and Legendre's equations.