The following functions return the value of the listed polynomial of degree n at x.

• hermite(n, x)—Hermite polynomial, or the solution of the following equation :
`d^2/dx^2 y-2x*dy/dx+2n*y=0`

• laguerre(n, x)—Laguerre polynomial, or the solution to the following equation :
`x*d^2/dx^2 y+(1-x)*dy/dx+n*y=0`

• legendre(n, x)—Legendre polynomial, or the solution to the following equation :
`(1-x^2)*d^2/dx^2 y-2x*dy/dx+n*(n+1)*y=0`

• chebyshevT(n, x)—Chebyshev of the first kind, or the solution to the following equation :
`(1-x^2)*d^2/dx^2 y-x*dy/dx+n^2*y=0`

• chebyshevU(n, x)—Chebyshev of the second kind, solution to the following equation :
`(1-x^2)*d^2/dx^2 y-3x*dy/dx+n*(n+2)*y=0`

• jacobi(n, a, b, x)—Jacobi with parameters a and b, solution to the following equation :
`(1-x^2)*d^2/dx^2 y+(b-a-(a+b+2)*x)*dy/dx+n*(n+a+b+1)*y=0`

Chebyshev and Legendre polynomials are special cases of the Jacobi polynomials:
chebyshevU(n, x) = jacobi(n, 0,1, x)
legendre(n, x) = jacobi(n, 0,0, x)

Arguments

• n is a nonnegative integer.
• x is a real scalar.
• a, b are real scalars greater than –1.