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Nov
10
accepted Frobenius Method for $x^4y''=y$
Nov
10
revised Frobenius Method for $x^4y''=y$
added 9 characters in body
Nov
10
asked Frobenius Method for $x^4y''=y$
Nov
2
accepted Laplaces Method not in standard form
Nov
2
comment Laplaces Method not in standard form
Thanks for the answer. I used @tired 's hint to get from the two points
Nov
2
comment Laplaces Method not in standard form
Yes I do mean $-\infty$
Nov
2
comment Laplaces Method not in standard form
Should I have that factor of x/k^2?
Nov
2
comment Laplaces Method not in standard form
Then my integrand becomes $\frac{x}{k^2}\exp[\sqrt x(k^2+1)/k^2]$
Nov
2
comment Laplaces Method not in standard form
I am trying to get there via laplace, but I am confused as to what I should use for h(x) and g(x) (in the Wiki page)
Nov
2
comment Laplaces Method not in standard form
Can I just go from the integral expression to the asymptotic expression?
Nov
2
asked Laplaces Method not in standard form
Nov
2
comment WKB Approximation of Legendre Equation
Or can I just use Frobenius's method? I see that it is valid in [-1,1] but will it suffice at infinity?
Nov
2
comment WKB Approximation of Legendre Equation
So looking at mathworld.wolfram.com/EulerDifferentialEquation.html I see that this will result in Bessel Equations. So should the asymptotics at infinity be similar to those at infinity?
Nov
2
comment WKB Approximation of Legendre Equation
I have come across method of dominant balance. Is that more appropriate?
Nov
2
revised WKB Approximation of Legendre Equation
added 12 characters in body
Nov
2
comment WKB Approximation of Legendre Equation
I failed to mention that $\nu ~O(1)$. Does that make a difference
Nov
2
asked WKB Approximation of Legendre Equation
Oct
26
comment Transformation of basis by diagonalization
Unfortunately that is all I know about M. That and it is real
Oct
26
comment Transformation of basis by diagonalization
Thats why I simplified the problem. For some reason I can't show that if our matrix is symmetric and real in one basis and diagonal in another than those bases are related...
Oct
26
comment Transformation of basis by diagonalization
Its for a problem in particle physics (M is actually a hamiltonian), so the identity matrix would be an uninteresting case for the problem