Campus Livre
jacobiP
Jacobi polynomial P_n^(a,b)(x).
Category: Mathematics > Polynomials
Syntax
P = jacobiP(n, a, b, x)Jacobi polynomial of degree n with parameters a and b.
Description
The Jacobi polynomials are orthogonal on [-1, 1] with weight (1 - x)^a*(1 + x)^b. They contain most classical families as special cases: a = b = 0 gives the Legendre polynomials, a = b = -1/2 gives a multiple of the Chebyshev polynomials of the first kind, and a = b gives the Gegenbauer polynomials up to scaling.
The first terms are P_0 = 1 and P_1 = (a - b)/2 + (a + b + 2)*x/2.
Input arguments
n- Degree, a nonnegative integer.
a, b- Parameters of the weight function; may be symbolic.
x- Point(s) of evaluation or a symbolic variable.
Output arguments
P- Numbers with the size of
x, or a symbolic polynomial.
Example
Special case and values
syms x
jacobiP(2, 0, 0, x)
jacobiP(2, 1, 1, x)
jacobiP(3, 1, 2, 0.5)Output
ans = (3*x^2)/2 - 1/2
ans = (15*x^2)/4 - 3/4
ans = -0.8125