On the fast computation of the Dirichlet-multinomial log-likelihood function

We introduce a new algorithm to compute the difference between values of the logΓ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\log \Gamma$$\end{document}-function in close points, where Γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma$$\end{document} denotes Euler’s gamma function. As a consequence, we obtain a way of computing the Dirichlet-multinomial log-likelihood function which is more accurate, has a better computational complexity and a wider range of application than the previously known ones.