On branched continued fraction expansions of hypergeometric functions \(F_M\) and their ratios
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 br...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Tuncer Acar
2025-03-01
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| Series: | Modern Mathematical Methods |
| Subjects: | |
| Online Access: | https://modernmathmeth.com/index.php/pub/article/view/52 |
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| Summary: | 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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| ISSN: | 3023-5294 |