Applying the mean value theorem for definite integrals in the non-linear integral equation for Chandrasekhar’s H function describing conservative isotropic scattering, we have derived a new, simple analytic approximation for it, with a maximal relative error below 2.5. With this new function as a starting-point, after a single iteration in the corresponding integral equation, we have obtained a new, highly accurate analytic approximation for the H function. As its maximal relative error is below 0.07, it significantly surpasses the accuracy of other analytic approximations.
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