Yeah you are right, there should be two partial symbols.
No problem with partial. As I stated above, I got the solution for this diff. eq.
(1-m^2y^2)f_{yy}-2my(i\lambda+m)f_{y}+(\lambda^2-im\lambda-\frac{k(k+1)}{y^2})f=0
from here
http://eqworld.ipmnet.ru/en/solutions/ode/ode0226.pdf...
Sorry in advance that I'm posting the same thing in two threads.
I really need it !
From Abramowitz's book I got this one
F(a, a+\frac{1}{2}, \frac{3}{2}, z^2)=\frac{1}{2}z^{-1}(1-2a)^{-1}[(1+z)^{1-2a}-(1-z)^{1-2a}]
Now I need to find
F(a, a+\frac{1}{2}, \frac{5}{2}...
Ok, I got the solution.
Now I need one thing. From Abramowitz's book I got this one
F(a, a+\frac{1}{2}, \frac{3}{2}, z^2)=\frac{1}{2}z^{-1}(1-2a)^{-1}[(1+z)^{1-2a}-(1-z)^{1-2a}]
Now I need to find
F(a, a+\frac{1}{2}, \frac{5}{2}, z^2)
F(a, a+\frac{1}{2}...
where
m, \lambda, k are constants.
I am trying to put these two:
f_1=\sum_{n=0}^{\infty}p_ny^{2n}, \ \ \ \ \ \ f_2=\sum_{n=0}^{\infty}a_ny^{2n+1}
and check if it is odd or even. At the end I am getting a recurrent eq.
any other ideas?
wups, thanks very much.
and another thing, I wrote wrong the above 2 eq.s, I put + instead of minus here
\lambda g(y)= i m y \frac{\partial g(y)}{\partial y} - \frac{\partial f(y)}{y} -\frac{k}{y}f
so it should be:
\lambda f(y)= i m y \frac{\partial f(y)}{\partial y} + \frac{\partial...
I somehow got this second oder diff.eq.
[tex]
(1-m^2y^2)f_{yy}-2my(i\lambda+m)f_{y}+(\lambda^2-im\lambda-\frac{k(k+1)}{y^2})f=0
[\tex]
where
[tex]f_{yy}[\tex] is [tex]\frac{\partial^2}{\partial y^2}[\tex]
Any ideas to solve this one?
p.s. Latex is not working here or am I...
\lambda f(y)= i b y \frac{\partial f(y)}{\partial y} + \frac{partial g(y)}{y} -\frac{k}{y}g
\lambda g(y)= i b y \frac{\partial g(y)}{\partial y} - \frac{partial f(y)}{y} +\frac{k}{y}f
I tried to get a hypergeometric eq. from these two but couldn't.
Any hints to solve?
Helps would be...