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JacobiP

  • JacobiP[ n , a , b , x ] gives the Jacobi polynomial .
  • Mathematical function (see Section A.3.10).
  • Explicit polynomials are given when possible.
  • satisfies the differential equation .
  • The Jacobi polynomials are orthogonal with weight function .
  • JacobiP[ n , a , b , z ] has a branch cut discontinuity in the complex z plane running from to .
  • See the Mathematica book: Section 3.2.9.
  • See also: LegendreP, ChebyshevT, ChebyshevU, GegenbauerC.

    Further Examples

    Here are the first five Jacobi polynomials.

    In[1]:=

    Out[1]=

    This is the derivative.

    In[2]:=

    Out[2]=

    This is the integral.

    In[3]:=

    Out[3]=

    This is a series expansion around .

    In[4]:=

    Out[4]=