On branched continued fraction expansions of hypergeometric functions \(F_M\) and their ratios
Keywords:
hypergeometric function, recurrence relation, branched continued fraction, approximation by rational functionsAbstract
The paper investigates the problem of constructing branched continued fraction expansions of hypergeometric functions \(F_M(a_1,a_2,b_1,b_2;a_1,c_2;\mathbf{z})\) and their ratios. Recurrence relations of the hypergeometric function \(F_M\) are established, which provide the construction of formal branched continued fractions with simple structures, the elements of which are polynomials in the variables \(z_1, z_2, z_3.\) To construct the expansions, a method of based on the so-called complete group of ratios of hypergeometric functions was used, which is a generalization of the classical Gauss method.
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Copyright (c) 2025 Ivan Nyzhnyk, Roman Dmytryshyn, Tamara Antonova
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