.. _scf_compute_coeffs_sphere: galpy.potential.scf_compute_coeffs_spherical ============================================= Note: This function computes Acos and Asin as defined in Hernquist & Ostriker (1992) _, except that we multiply Acos by 2 such that the density from :ref:Galpy's Hernquist Potential  corresponds to :math:Acos = \delta_{0n}\delta_{0l}\delta_{0m}. Futher note that this function is a specification of :ref:scf_compute_coeffs_axi  where :math:Acos_{nlm} = 0 \ at :math:l\neq0 For a given :math:\rho(r) we can compute :math:Acos and :math:Asin through the following equation .. math:: Acos_{nlm}= \frac{16 \pi a^3}{I_{nl}} \int_{\xi=0}^{\infty} (1 + \xi)^{2} (1 - \xi)^{-4} \rho(r) \Phi_{nlm}(\xi) d\xi \qquad Asin_{nlm}=None Where .. math:: \Phi_{nlm}(\xi, \cos(\theta)) = -\frac{1}{2 a} (1 - \xi) C_{n}^{3/2}(\xi) \delta_{l0} \delta_{m0} .. math:: I_{n0} = - K_{n0} \frac{1}{4 a} \frac{(n + 2) (n + 1)}{(n + 3/2)} \qquad K_{nl} = \frac{1}{2}n(n + 3) + 1 :math:C_{n}^{\alpha} is the Gegenbauer polynomial. Also note :math:\xi = \frac{r - a}{r + a}, and :math:n, :math:l and :math:m are integers bounded by :math:0 <= n < N , :math:l = m = 0 .. autofunction:: galpy.potential.scf_compute_coeffs_spherical