There are two independent solutions which are given as series by:
In each case, the coefficients are given by the recursion
with arising from the choice , , and arising from the choice , .
When is a non-negative integer, one of these series will terminate, giving a polynomial solution. If is even, then the series for terminates at . If is odd, then the series for terminates at .
(In fact, polynomial solutions are also obtained when is a negative integer, but these are not new solutions, since the Chebyshev equation is invariant under the substitution of by .)
|Date of creation||2013-03-22 13:10:17|
|Last modified on||2013-03-22 13:10:17|
|Last modified by||mclase (549)|
|Synonym||Chebyshev differential equation|