This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)

JacobiP

JacobiP[n, a, b, x]
gives the Jacobi polynomial .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • Explicit polynomials are given when possible.
  • satisfies the differential equation (1-x^2)y^(′′)+(b-a-(a+b+2)x)y^′+n(n+a+b+1)y=0.
  • The Jacobi polynomials are orthogonal with weight function (1-x)^a(1+x)^b.
  • For certain special arguments, JacobiP automatically evaluates to exact values.
  • JacobiP can be evaluated to arbitrary numerical precision.
  • JacobiP automatically threads over lists.
  • JacobiP[n, a, b, z] has a branch cut discontinuity in the complex z plane running from -∞ to -1.
New in 1