https://oldena.lpnu.ua/handle/ntb/41472| Title: | The algorithms of constructing the continued fractions for any rations of the hypergeometric Gaussian functions |
| Other Titles: | Алгоритми побудови неперервних дробів для довільних відношень гіпергеометричних функцій Гаусса |
| Authors: | Манзій, О. Гладун, В. Вентик, Л. Manziy, O. Hladun, V. Ventyk, L. |
| Affiliation: | Національний унівеpситет «Львівська політехніка» Lviv Polytechnic National University |
| Bibliographic description (Ukraine): | Manziy O. The algorithms of constructing the continued fractions for any rations of the hypergeometric Gaussian functions / O. Manziy, V. Hladun, L. Ventyk // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2017. — Vol 4. — No 1. — P. 48–58. |
| Bibliographic description (International): | Manziy O. The algorithms of constructing the continued fractions for any rations of the hypergeometric Gaussian functions / O. Manziy, V. Hladun, L. Ventyk // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2017. — Vol 4. — No 1. — P. 48–58. |
| Is part of: | Mathematical Modeling and Computing, 1 (4), 2017 |
| Issue: | 1 |
| Volume: | 4 |
| Issue Date: | 15-Jun-2017 |
| Publisher: | Lviv Politechnic Publishing House |
| Place of the edition/event: | Lviv |
| UDC: | 517.526 519.688 |
| Keywords: | гіпергеометричний ряд Гаусса гіпергеометрична функція неперервний дріб рекурентне відношення розвинення відношення алгоритм наближення Gaussian hypergeometric series hypergeometric function continued fraction recurrence relation expansion ratio algorithm approximant |
| Number of pages: | 11 |
| Page range: | 48-58 |
| Start page: | 48 |
| End page: | 58 |
| Abstract: | Описано алгоритм побудови рекурентних спiввiдношень гiпергеометричних функцiй
Гаусса, в яких змiщення параметрiв a, b, c дорiвнює 0, 1 або −1. На основi таких
рекурентних спiввiдношень побудовано розвинення для вiдношення функцiй Гаусса
у неперервнi дроби. Отриманi неперервнi дроби є розвиненням вiдповiдних гiпергео-
метричних функцiй Гаусса, якщо параметри функцiї є цiлими числами. An algorithm for constructing recurrence relations of geometric Gaussian functions, in which the displacement of parameters is equal to 0, 1 or −1, is described. On the basis of such recurrence relations, the expansion for the ratio of Gaussian functions into continued fractions is developed. The obtained continued fractions are the development of the corresponding hypergeometric Gaussian functions in the case when the parameters of the function are integers. |
| URI: | https://ena.lpnu.ua/handle/ntb/41472 |
| ISSN: | 2312-9794 |
| Copyright owner: | © 2017 Lviv Polytechnic National University CMM IAPMM NASU |
| References (Ukraine): | [1] AbramovvitzM., Stegun I.A. Handbook of mathematical functions with formulas, grapth and mathematical tables. NBS (1972). [2] BatemanH., Erd´elyiA. Higher transcendental functions. Vol.1, Moscow, Nauka, 295 p. (1973), (in Russian). [3] LebedevN. Special functions and their applications. Mosсow-Leningrad, Fizmatgiz, 630 p. (1963), (in Russian). [4] LukeY. Special mathematical functions and their approximation. Moscow, Mir, 608 p. (1980), (in Russian). [5] ChuluunbaatarO. Mathematical models and logarithms for the analysis of processes of ionization of helium atoms and hydrogen molecules with variational functions. Bulletin of the TvGU. Series: Applied Mathematics. 47–64 (2008), (in Rusiian). [6] ExtonH. Multiple hypergeometric functions and applications. New York, Sydney, Toronto, Chichester, Ellis Hoorwood, 376 p. (1976). [7] VerlanA., SizikovV. Integral equation methods, algorithms, programs. Kyiv, Naukova Dumka, 544 p. (1986), (in Ukrainian). [8] PopovB., TeslerH. The calculation functions on the computer: Directory. Kyiv, Naukova Dumka, 600 p. (1984), (in Russian). [9] ManziyO., HladunV., PabirivskyV., UhanskaO. Algorithms for calculating the value of some hypergeometric Gaussian function in the complex plane. Physical and mathematical modeling and information technologies. Iss. 19, 17–26 (2014), (in Ukrainian). [10] CuytA., PetersenV.B., VerdonkB., WaadelandH., JonesW.B. Handbook of Continued Fractions for Special Functions. Berlin, Springer, 431 p. (2008). [11] WilliamB. J., ThronW. J. Continued fractions. Analytic theory and applications. Vol. 2. Moscow, Mir, 414 p. (1985), (in Russian). [12] Lorentzen L., WaadelamdH. Continued Fractions. Convergence Theory. Atlantis Press World Scientific, Amsterdam, Paris, 308 p. (2008). |
| References (International): | [1] AbramovvitzM., Stegun I.A. Handbook of mathematical functions with formulas, grapth and mathematical tables. NBS (1972). [2] BatemanH., Erd´elyiA. Higher transcendental functions. Vol.1, Moscow, Nauka, 295 p. (1973), (in Russian). [3] LebedevN. Special functions and their applications. Mossow-Leningrad, Fizmatgiz, 630 p. (1963), (in Russian). [4] LukeY. Special mathematical functions and their approximation. Moscow, Mir, 608 p. (1980), (in Russian). [5] ChuluunbaatarO. Mathematical models and logarithms for the analysis of processes of ionization of helium atoms and hydrogen molecules with variational functions. Bulletin of the TvGU. Series: Applied Mathematics. 47–64 (2008), (in Rusiian). [6] ExtonH. Multiple hypergeometric functions and applications. New York, Sydney, Toronto, Chichester, Ellis Hoorwood, 376 p. (1976). [7] VerlanA., SizikovV. Integral equation methods, algorithms, programs. Kyiv, Naukova Dumka, 544 p. (1986), (in Ukrainian). [8] PopovB., TeslerH. The calculation functions on the computer: Directory. Kyiv, Naukova Dumka, 600 p. (1984), (in Russian). [9] ManziyO., HladunV., PabirivskyV., UhanskaO. Algorithms for calculating the value of some hypergeometric Gaussian function in the complex plane. Physical and mathematical modeling and information technologies. Iss. 19, 17–26 (2014), (in Ukrainian). [10] CuytA., PetersenV.B., VerdonkB., WaadelandH., JonesW.B. Handbook of Continued Fractions for Special Functions. Berlin, Springer, 431 p. (2008). [11] WilliamB. J., ThronW. J. Continued fractions. Analytic theory and applications. Vol. 2. Moscow, Mir, 414 p. (1985), (in Russian). [12] Lorentzen L., WaadelamdH. Continued Fractions. Convergence Theory. Atlantis Press World Scientific, Amsterdam, Paris, 308 p. (2008). |
| Content type: | Article |
| Appears in Collections: | Mathematical Modeling And Computing. – 2017. – Vol. 4, No. 1 |
| File | Description | Size | Format | |
|---|---|---|---|---|
| 2017v4n1_Manziy_O-The_algorithms_of_constructing_48-58.pdf | 1.13 MB | Adobe PDF | View/Open | |
| 2017v4n1_Manziy_O-The_algorithms_of_constructing_48-58__COVER.png | 402.06 kB | image/png | View/Open |
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