On convergence of function F4(1, 2; 2, 2; z1, z2) expansion into a branched continued fraction

Simple item page
dc.citation.epage778
dc.citation.issue3
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage767
dc.contributor.affiliationНаціональний університет “Львівська політехніка”
dc.contributor.affiliationІнститут прикладних проблем механіки і метематики ім. Я. С. Підстригача НАН України
dc.contributor.affiliationLviv Polytechnic National University
dc.contributor.affiliationPidstryhach Institute for Applied Problems of Mechanics and Mathematics
dc.contributor.authorГладун, В. Р.
dc.contributor.authorГоєнко, Н. П.
dc.contributor.authorМанзій, О. С.
dc.contributor.authorВентик, Л. С.
dc.contributor.authorHladun, V. R.
dc.contributor.authorHoyenko, N. P.
dc.contributor.authorManziy, O. S.
dc.contributor.authorVentyk, L. S.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-03-04T11:33:03Z
dc.date.created2022-02-28
dc.date.issued2022-02-28
dc.description.abstractУ роботі проаналізовано можливість наближення гіпергеометричної функції Аппеля F4(1, 2; 2, 2; z1, z2) гіллястим ланцюговим дробом спеціального вигляду. Доведено відповідність побудованого гіллястого ланцюгового дробу до гіпергеометричної функції Аппеля F4. Встановлено збіжність отриманого гіллястого ланцюгового дробу у деякій полікруговій області двовимірного комплексного простору та проведено чисельні експерименти. Результати обчислень підтвердили ефективність апроксимації гіпергеометричної функції Аппеля F4(1, 2; 2, 2; z1, z2) за допомогою гіллястого ланцюгового дробу спеціального вигляду та проілюстрували гіпотезу існування ширшої області збіжності отриманого розвинення.
dc.description.abstractIn the paper, the possibility of the Appell hypergeometric function F4(1,2;2,2;z1,z2) approximation by a branched continued fraction of a special form is analysed. The correspondence of the constructed branched continued fraction to the Appell hypergeometric function F4 is proved. The convergence of the obtained branched continued fraction in some polycircular domain of two-dimensional complex space is established, and numerical experiments are carried out. The results of the calculations confirmed the efficiency of approximating the Appell hypergeometric function F4(1,2;2,2;z1,z2) by a branched continued fraction of special form and illustrated the hypothesis of the existence of a wider domain of convergence of the obtained expansion.
dc.format.extent767-778
dc.format.pages12
dc.identifier.citationOn convergence of function F4(1, 2; 2, 2; z1, z2) expansion into a branched continued fraction / V. R. Hladun, N. P. Hoyenko, O. S. Manziy, L. S. Ventyk // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 3. — P. 767–778.
dc.identifier.citationenOn convergence of function F4(1, 2; 2, 2; z1, z2) expansion into a branched continued fraction / V. R. Hladun, N. P. Hoyenko, O. S. Manziy, L. S. Ventyk // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 3. — P. 767–778.
dc.identifier.doidoi.org/10.23939/mmc2022.03.767
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/63473
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 3 (9), 2022
dc.relation.ispartofMathematical Modeling and Computing, 3 (9), 2022
dc.relation.references[1] Exton H. Multiple hypergeometric functions and applications. New York – Sydney – Toronto, Chichester, Ellis Horwood (1976).
dc.relation.references[2] Huber T., Maitre D. HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters. Computer Physics Communications. 178 (10), 755–776 (2008).
dc.relation.references[3] Bytev V. V., Kalmykov M. Yu., Kniehl B. A. Differential reduction of generalized hypergeometric functions from Feynman diagrams: One-variable case. Nuclear Physics B. 836 (3), 129–170 (2010).
dc.relation.references[4] Feng T.-F., Chang C.-H., Chen J.-B., Gu Z.-H., Zhang H.-B. Evaluating Feynman integrals by the hypergeometry. Nuclear Physics B. 927, 516–549 (2018).
dc.relation.references[5] Bateman H., Erdelyi A. Higher Transcendental Functions, Volume I. New York, McGraw-Hill Book Co., Inc. (1953).
dc.relation.references[6] Luke Y. Special mathematical functions and their approximation. Moscow, Mir (1980), (in Russian).
dc.relation.references[7] Kalmykov M. Yu., Kniehl B. A. Mellin–Barnes representations of Feynman diagrams, linear systems of differential equations, and polynomial solutions. Phys. Lett. B. 714 (1), 103–109 (2012).
dc.relation.references[8] Jones William B., Thron W. J. Continued fractions. Analytic theory and applications (Encyclopedia of Mathematics and its Applications, Series Number 11). Cambridge, Cambridge University Press (2009).
dc.relation.references[9] Cuyt A., Petersen V. B., Vendonk B., Waadeland H., Jones W. B. Handbook of Continued Fractions for Special Functions. Berlin, Springer (2008).
dc.relation.references[10] Lorentzen L., Waadeland H. Continued Fractions with Application, Studies in Computational Mathematics, Volume 3. Amsterdam, North-Holland (1992).
dc.relation.references[11] Appell P., Kampe de Feriet J. Fonctions hypergeometriques et hyperspheriques. Polinomes d’Hermite. Paris, Couthier-Villars (1926), (in French).
dc.relation.references[12] Bodnarchuk P. I., Skorobohat’ko V. Ya. Branched Continued Fractions and Their Applications. Kyiv, Naukova dumka (1974), (in Ukrainian).
dc.relation.references[13] Bodnar D. I. The multivariable C-fractions. Mat. Metody Fiz. Mekh. Polya. 39 (2), 39–46 (1996), (in Ukrainian).
dc.relation.references[14] Bodnar D. I. Branched continued fractions. Kyiv, Naukova dumka (1986), (in Russian).
dc.relation.references[15] Manziy O. S., Hladun V. R., Ventyk L. S. The algorithms of constructing the continued fractions for any rations of the hypergeometric Gaussian functions. Mathematical Modeling and Computing. 4 (1), 48–58 (2017).
dc.relation.references[16] Hoyenko N., Antonova T., Rakintsev S. Approximation for ratios of Lauricella–Saran fuctions Fs with real parameters by a branched continued fractions. Math. Bul. Shevchenko Sci. Soc. 8, 28–42 (2011), (in Ukrainian).
dc.relation.references[17] Antonova T., Dmytryshyn R., Kravtsiv V. Branched Continued Fraction Expansions of Horn’s Hypergeometric Function H3 Ratios. Mathematics. 9 (2), 148 (2021).
dc.relation.references[18] Hoyenko N. P., Hladun V. R., Manzij O. S. On the infinite remains of the Norlund branched continued fraction for Appell hypergeometric functions. Carpathian Mathematical Publications. 6 (1), 11–25 (2014).
dc.relation.references[19] Hoyenko N. P. Correspondence principle and convergence of sequences of analytic functions of several variables. Math. Bull. Shevchenko Sci. Soc. 4, 42–48 (2007), (in Ukrainian).
dc.relation.references[20] Hladun V. R., Hoyenko N. P., Ventyk L. S., Manziy O. S. About the calculation of hypergeometric function F4(1, 2; 2, 2; z1, z2) by the branched continued fraction of a special kind. Physico-mathematical modeling and informational technologies. 32, 86–90 (2021), (in Ukrainian).
dc.relation.referencesen[1] Exton H. Multiple hypergeometric functions and applications. New York – Sydney – Toronto, Chichester, Ellis Horwood (1976).
dc.relation.referencesen[2] Huber T., Maitre D. HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters. Computer Physics Communications. 178 (10), 755–776 (2008).
dc.relation.referencesen[3] Bytev V. V., Kalmykov M. Yu., Kniehl B. A. Differential reduction of generalized hypergeometric functions from Feynman diagrams: One-variable case. Nuclear Physics B. 836 (3), 129–170 (2010).
dc.relation.referencesen[4] Feng T.-F., Chang C.-H., Chen J.-B., Gu Z.-H., Zhang H.-B. Evaluating Feynman integrals by the hypergeometry. Nuclear Physics B. 927, 516–549 (2018).
dc.relation.referencesen[5] Bateman H., Erdelyi A. Higher Transcendental Functions, Volume I. New York, McGraw-Hill Book Co., Inc. (1953).
dc.relation.referencesen[6] Luke Y. Special mathematical functions and their approximation. Moscow, Mir (1980), (in Russian).
dc.relation.referencesen[7] Kalmykov M. Yu., Kniehl B. A. Mellin–Barnes representations of Feynman diagrams, linear systems of differential equations, and polynomial solutions. Phys. Lett. B. 714 (1), 103–109 (2012).
dc.relation.referencesen[8] Jones William B., Thron W. J. Continued fractions. Analytic theory and applications (Encyclopedia of Mathematics and its Applications, Series Number 11). Cambridge, Cambridge University Press (2009).
dc.relation.referencesen[9] Cuyt A., Petersen V. B., Vendonk B., Waadeland H., Jones W. B. Handbook of Continued Fractions for Special Functions. Berlin, Springer (2008).
dc.relation.referencesen[10] Lorentzen L., Waadeland H. Continued Fractions with Application, Studies in Computational Mathematics, Volume 3. Amsterdam, North-Holland (1992).
dc.relation.referencesen[11] Appell P., Kampe de Feriet J. Fonctions hypergeometriques et hyperspheriques. Polinomes d’Hermite. Paris, Couthier-Villars (1926), (in French).
dc.relation.referencesen[12] Bodnarchuk P. I., Skorobohat’ko V. Ya. Branched Continued Fractions and Their Applications. Kyiv, Naukova dumka (1974), (in Ukrainian).
dc.relation.referencesen[13] Bodnar D. I. The multivariable C-fractions. Mat. Metody Fiz. Mekh. Polya. 39 (2), 39–46 (1996), (in Ukrainian).
dc.relation.referencesen[14] Bodnar D. I. Branched continued fractions. Kyiv, Naukova dumka (1986), (in Russian).
dc.relation.referencesen[15] Manziy O. S., Hladun V. R., Ventyk L. S. The algorithms of constructing the continued fractions for any rations of the hypergeometric Gaussian functions. Mathematical Modeling and Computing. 4 (1), 48–58 (2017).
dc.relation.referencesen[16] Hoyenko N., Antonova T., Rakintsev S. Approximation for ratios of Lauricella–Saran fuctions Fs with real parameters by a branched continued fractions. Math. Bul. Shevchenko Sci. Soc. 8, 28–42 (2011), (in Ukrainian).
dc.relation.referencesen[17] Antonova T., Dmytryshyn R., Kravtsiv V. Branched Continued Fraction Expansions of Horn’s Hypergeometric Function H3 Ratios. Mathematics. 9 (2), 148 (2021).
dc.relation.referencesen[18] Hoyenko N. P., Hladun V. R., Manzij O. S. On the infinite remains of the Norlund branched continued fraction for Appell hypergeometric functions. Carpathian Mathematical Publications. 6 (1), 11–25 (2014).
dc.relation.referencesen[19] Hoyenko N. P. Correspondence principle and convergence of sequences of analytic functions of several variables. Math. Bull. Shevchenko Sci. Soc. 4, 42–48 (2007), (in Ukrainian).
dc.relation.referencesen[20] Hladun V. R., Hoyenko N. P., Ventyk L. S., Manziy O. S. About the calculation of hypergeometric function F4(1, 2; 2, 2; z1, z2) by the branched continued fraction of a special kind. Physico-mathematical modeling and informational technologies. 32, 86–90 (2021), (in Ukrainian).
dc.rights.holder© Національний університет “Львівська політехніка”, 2022
dc.subjectгіпергеометричний ряд
dc.subjectгіпергеометрична функція Аппеля
dc.subjectрекурентне відношення
dc.subjectнеперервний дріб
dc.subjectгіллястий ланцюговий дріб
dc.subjectобласть збіжності
dc.subjectвідповідність
dc.subjecthypergeometric series
dc.subjectAppell hypergeometric function
dc.subjectrecurrence relation
dc.subjectcontinued fraction
dc.subjectbranched continued fraction
dc.subjectconvergence domain
dc.subjectcorrespondence
dc.titleOn convergence of function F4(1, 2; 2, 2; z1, z2) expansion into a branched continued fraction
dc.title.alternativeПро збіжність розвинення функції F4(1, 2; 2, 2; z1, z2) в гіллястий ланцюговий дріб
dc.typeArticle

Files

Original bundle

Now showing 1 - 2 of 2
Thumbnail Image
Name:
2022v9n3_Hladun_V_R-On_convergence_of_function_767-778.pdf
Size:
1.61 MB
Format:
Adobe Portable Document Format
Download
Thumbnail Image
Name:
2022v9n3_Hladun_V_R-On_convergence_of_function_767-778__COVER.png
Size:
437.16 KB
Format:
Portable Network Graphics
Download

License bundle

Now showing 1 - 1 of 1
Thumbnail Image
Name:
license.txt
Size:
1.87 KB
Format:
Plain Text
Description:
Download

Collections

Mathematical Modeling And Computing. – 2022. – Vol. 9, No. 3