.. _scf_compute_coeffs_axi: galpy.potential.scf_compute_coeffs_axi ======================================== 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}. Further note that this function is a specification of :ref:scf_compute_coeffs  where :math:Acos_{nlm} = 0 \ at :math:m\neq0 and :math:Asin_{nlm} = None For a given :math:\rho(R, z) we can compute :math:Acos and :math:Asin through the following equation .. math:: Acos_{nlm}= \frac{8 \pi a^3}{I_{nl}} \int_{\xi=0}^{\infty} \int_{\cos(\theta)=-1}^{1} (1 + \xi)^{2} (1 - \xi)^{-4} \rho(R, z) \Phi_{nlm}(\xi, \cos(\theta)) d\cos(\theta) d\xi \qquad Asin_{nlm}=None Where .. math:: \Phi_{nlm}(\xi, \cos(\theta)) = -\frac{\sqrt{2l + 1}}{a2^{2l + 1}} (1 + \xi)^l (1 - \xi)^{l + 1} C_{n}^{2l + 3/2}(\xi) P_{l0}(\cos(\theta)) \delta_{m0} .. math:: I_{nl} = - K_{nl} \frac{4\pi}{a 2^{8l + 6}} \frac{\Gamma(n + 4l + 3)}{n! (n + 2l + 3/2)[\Gamma(2l + 3/2)]^2} \qquad K_{nl} = \frac{1}{2}n(n + 4l + 3) + (l + 1)(2l + 1) :math:P_{lm} is the Associated Legendre Polynomials whereas :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:0 <= l < L, and :math:m = 0 .. autofunction:: galpy.potential.scf_compute_coeffs_axi