Spherical harmonics Y_lm in C

spherical_harmonics.c

#include <stdio.h>
#include <gsl/gsl_sf_legendre.h>
#include <gsl/gsl_sf_result.h>

int main() {
    double theta = 1.2; // Example value for theta
    double phi = 0.8;   // Example value for phi
    int l = 2;          // Spherical harmonic degree
    int m = 1;          // Spherical harmonic order

    gsl_sf_result result;
    gsl_sf_legendre_sphPlm_e(l, m, cos(theta), &result);

    double Y_lm = result.val * cos(m * phi); // Real part of Y_lm

    printf("Y_%d%d(%f, %f) = %f\n", l, m, theta, phi, Y_lm);
    return 0;
}