The equation is named after Russian mathematician Pafnuty Chebyshev.
(note, x may be complex), as may be seen by applying the ratio test to the recurrence.
The recurrence may be started with arbitrary values of a0 and a1, leading to the two-dimensional space of solutions that arises from second order differential equations.
The standard choices are: and The general solution is any linear combination of these two.
In this case, that function is a polynomial of degree p and it is proportional to the Chebyshev polynomial of the first kind This article incorporates material from Chebyshev equation on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.