Compact Formulation for Numerical Solution of Chandrasekhar’s $$\boldsymbol{H}$$-Function

Chandrasekhar’s $$H$$ -function plays an important role in applied sciences, such as radiative transfer scattering theory. In this paper a numerical solution of the nonlinear integral equation for Chandrasekhar’s $$H$$ -function and its first derivative has been derived. In addition, numerical results for the zeroth, first, and second moments of the $$H$$ -function are obtained. We have arranged a compact formulation for the Gauss-shifted Legendre quadrature set and used it for numerical computation. It can be seen from the derivation of the equations and application of the numerical method explained in detail that the present method can be applied to other problems in applied sciences. Numerical results consistent with those available in the literature have been obtained even in low-order approximations. Accordance between them corresponds to a difference of about 0.01 $$\%$$ . This explicitly illustrates the accuracy and capability of the method.