chebyshev_U( n , z )

The Chebyshev polynomial of the second kind of z in SageMath. A solution of the differential equation

$( 1-z^2 ) \frac{ d^2 f }{ dz^2 } -3z \frac{ d f }{ dz } + n(n+2) f = 0$

Explicit form:

Plot on the real axis:

Special values:

Related functions:   chebyshev_T

Function category: orthogonal polynomials sagemath-docs