finesse.utilities.homs.jacobi_real_x

finesse.utilities.homs.jacobi_real_x(n, a, b, x)

Jacobi Polynomial P_n^{a,b}(x) for real x.

n / n+a / n+b / x-1 ^(s) / x+1 ^(n-s)

P_n^{a,b}(x)= Sum | | | | | — | | — |

s=0 n-s / s / 2 / 2 /

Parameters:

n, a, bint

Polynomial coefficients

xfloat

Polynomial argument

Notes

Implementation of Jacobi fucntion using binominal coefficients. This can handle values of alpha, beta < -1 which the special.eval_jacobi function does not.