3
$\begingroup$

Find a power series solution about $x_0=0$ for the Chebyshev differential equation $$(1-x^2)y''-xy'+n^2 y=0,$$ as a function of of the integer $n$. Show that the solutions form a terminating expansion for each value of $n$. What is the orthogonality relationship for these polynomials?

  • 2
    Welcome to math.stackexchange! In order to make the answers helpful for you, you should tell us what you tried and where you are stuck.2012-09-27
  • 0
    [Here](http://www.math.ksu.edu/math240/math240.s09/chap4part1.pdf) is a detailed solution.2012-09-27
  • 0
    @DavideGiraudo I think I solved for the power series expansion first and got this as my recurrence relation. 0=a_(n+2) (n+2)(n+1)+(h^2-n^2 ) a_n Not sure where to go from there as all my coefficients turned out really wild.2012-09-27
  • 0
    What is $h$ here?2012-09-27
  • 0
    sorry to avoid confusing myself, I changed the n in the primary equation to an h2012-09-27

1 Answers 1