yankeefan11
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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