The algorithms of constructing the continued fractions for any rations of the hypergeometric Gaussian functions

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dc.citation.epage58
dc.citation.issue1
dc.citation.spage48
dc.citation.volume4
dc.contributor.affiliationНаціональний унівеpситет «Львівська політехніка»
dc.contributor.affiliationLviv Polytechnic National University
dc.contributor.authorМанзій, О.
dc.contributor.authorГладун, В.
dc.contributor.authorВентик, Л.
dc.contributor.authorManziy, O.
dc.contributor.authorHladun, V.
dc.contributor.authorVentyk, L.
dc.coverage.placenameLviv
dc.date.accessioned2018-06-05T14:12:28Z
dc.date.available2018-06-05T14:12:28Z
dc.date.created2017-06-15
dc.date.issued2017-06-15
dc.description.abstractОписано 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.
dc.description.abstractAn 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.
dc.format.extent48-58
dc.format.pages11
dc.identifier.citationManziy 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.
dc.identifier.citationenManziy 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.
dc.identifier.issn2312-9794
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/41472
dc.language.isoen
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofMathematical Modeling and Computing, 1 (4), 2017
dc.relation.references[1] AbramovvitzM., Stegun I.A. Handbook of mathematical functions with formulas, grapth and mathematical tables. NBS (1972).
dc.relation.references[2] BatemanH., Erd´elyiA. Higher transcendental functions. Vol.1, Moscow, Nauka, 295 p. (1973), (in Russian).
dc.relation.references[3] LebedevN. Special functions and their applications. Mosсow-Leningrad, Fizmatgiz, 630 p. (1963), (in Russian).
dc.relation.references[4] LukeY. Special mathematical functions and their approximation. Moscow, Mir, 608 p. (1980), (in Russian).
dc.relation.references[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).
dc.relation.references[6] ExtonH. Multiple hypergeometric functions and applications. New York, Sydney, Toronto, Chichester, Ellis Hoorwood, 376 p. (1976).
dc.relation.references[7] VerlanA., SizikovV. Integral equation methods, algorithms, programs. Kyiv, Naukova Dumka, 544 p. (1986), (in Ukrainian).
dc.relation.references[8] PopovB., TeslerH. The calculation functions on the computer: Directory. Kyiv, Naukova Dumka, 600 p. (1984), (in Russian).
dc.relation.references[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).
dc.relation.references[10] CuytA., PetersenV.B., VerdonkB., WaadelandH., JonesW.B. Handbook of Continued Fractions for Special Functions. Berlin, Springer, 431 p. (2008).
dc.relation.references[11] WilliamB. J., ThronW. J. Continued fractions. Analytic theory and applications. Vol. 2. Moscow, Mir, 414 p. (1985), (in Russian).
dc.relation.references[12] Lorentzen L., WaadelamdH. Continued Fractions. Convergence Theory. Atlantis Press World Scientific, Amsterdam, Paris, 308 p. (2008).
dc.relation.referencesen[1] AbramovvitzM., Stegun I.A. Handbook of mathematical functions with formulas, grapth and mathematical tables. NBS (1972).
dc.relation.referencesen[2] BatemanH., Erd´elyiA. Higher transcendental functions. Vol.1, Moscow, Nauka, 295 p. (1973), (in Russian).
dc.relation.referencesen[3] LebedevN. Special functions and their applications. Mossow-Leningrad, Fizmatgiz, 630 p. (1963), (in Russian).
dc.relation.referencesen[4] LukeY. Special mathematical functions and their approximation. Moscow, Mir, 608 p. (1980), (in Russian).
dc.relation.referencesen[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).
dc.relation.referencesen[6] ExtonH. Multiple hypergeometric functions and applications. New York, Sydney, Toronto, Chichester, Ellis Hoorwood, 376 p. (1976).
dc.relation.referencesen[7] VerlanA., SizikovV. Integral equation methods, algorithms, programs. Kyiv, Naukova Dumka, 544 p. (1986), (in Ukrainian).
dc.relation.referencesen[8] PopovB., TeslerH. The calculation functions on the computer: Directory. Kyiv, Naukova Dumka, 600 p. (1984), (in Russian).
dc.relation.referencesen[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).
dc.relation.referencesen[10] CuytA., PetersenV.B., VerdonkB., WaadelandH., JonesW.B. Handbook of Continued Fractions for Special Functions. Berlin, Springer, 431 p. (2008).
dc.relation.referencesen[11] WilliamB. J., ThronW. J. Continued fractions. Analytic theory and applications. Vol. 2. Moscow, Mir, 414 p. (1985), (in Russian).
dc.relation.referencesen[12] Lorentzen L., WaadelamdH. Continued Fractions. Convergence Theory. Atlantis Press World Scientific, Amsterdam, Paris, 308 p. (2008).
dc.rights.holder© 2017 Lviv Polytechnic National University CMM IAPMM NASU
dc.subjectгіпергеометричний ряд Гаусса
dc.subjectгіпергеометрична функція
dc.subjectнеперервний дріб
dc.subjectрекурентне відношення
dc.subjectрозвинення
dc.subjectвідношення
dc.subjectалгоритм
dc.subjectнаближення
dc.subjectGaussian hypergeometric series
dc.subjecthypergeometric function
dc.subjectcontinued fraction
dc.subjectrecurrence relation
dc.subjectexpansion
dc.subjectratio
dc.subjectalgorithm
dc.subjectapproximant
dc.subject.udc517.526
dc.subject.udc519.688
dc.titleThe algorithms of constructing the continued fractions for any rations of the hypergeometric Gaussian functions
dc.title.alternativeАлгоритми побудови неперервних дробів для довільних відношень гіпергеометричних функцій Гаусса
dc.typeArticle

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Mathematical Modeling And Computing. – 2017. – Vol. 4, No. 1