Chebyshev equation

Chebyshev's equation is the second order linear differential equation Chebyshev's equation is the second order linear differential equation where p is a real (or complex) constant. The equation is named after Russian mathematician Pafnuty Chebyshev. The solutions can be obtained by power series: where the coefficients obey the recurrence relation The series converges for | x | < 1 {displaystyle |x|<1} (note, x may be complex), as may be seen by applyingthe 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 orderdifferential equations. The standard choices are: