- #1
KateyLou
- 17
- 0
Homework Statement
Obtain the recurrene relation between the coefficient ar in the series solution
y= (between r=0 and [tex]\infty[/tex]) [tex]\Sigma[/tex] arxr
to (1-x2)y''-2xy'+k(k+1)y=0
Deduce that if k is a positive integer, then ak+2=0, so that the equation possesses a solution which is a polynomial of degree k.
Homework Equations
(there is more to this question...but i think ill try getting through this bit first!)
The Attempt at a Solution
I have managed to get the correct recurrance relation
(n+2)(n+1)an+2-an(n(n+1)-k(k+1))=0
But i have no idea what to do now (the show if k is a positive integer) etc :-(