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JacobiP

JacobiP
gives the Jacobi polynomial .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • Explicit polynomials are given when possible.
  • satisfies the differential equation .
  • The Jacobi polynomials are orthogonal with weight function .
  • For certain special arguments, JacobiP automatically evaluates to exact values.
  • JacobiP can be evaluated to arbitrary numerical precision.
  • JacobiP automatically threads over lists.
  • JacobiP has a branch cut discontinuity in the complex z plane running from to .
Compute the 2^(nd) Jacobi polynomial:
Plot :
Compute the 2^(nd) Jacobi polynomial:
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Click for copyable input
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Plot :
In[1]:=
Click for copyable input
Out[1]=
Evaluate for fractional orders:
Evaluate for complex orders and arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Simple cases give exact symbolic results:
JacobiP threads element-wise over lists:
TraditionalForm formatting:
Expected value of the number of real eigenvalues of a complex matrix:
Solve a Jacobi differential equation:
Solution of the Schrödinger equation with a Pöschl-Teller potential:
Calculate the energy eigenvalue from the differential equation:
Use FunctionExpand to expand into other functions:
Cancellations in the polynomial form may lead to inaccurate numerical results:
Evaluate the function directly:
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