﻿﻿ math handbook calculator - Fractional Calculus Computer Algebra System software
+ + + =

﻿
Functions > Complex Functions > Special Functions > Polynomial Functions

# Polynomial Functions

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.

## Related Topics

Complex Functions
Special Functions
Example : Polynomial Functions ﻿