Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2024, , 11 - 26, 16.12.2024
https://doi.org/10.33205/cma.1545452

Öz

Kaynakça

  • T. Antonova, C. Cesarano, R. Dmytryshyn and S. Sharyn: An approximation to Appell’s hypergeometric function F2 by branched continued fraction, Dolomites Res. Notes Approx., 17 (1) (2024), 22–31.
  • T. Antonova, R. Dmytryshyn and V. Goran: On the analytic continuation of Lauricella-Saran hypergeometric function FK(a1, a2, b1, b2; a1, b2, c3; z), Mathematics, 11 (21) (2023), Article ID: 4487.
  • T. Antonova, R. Dmytryshyn and V. Kravtsiv: Branched continued fraction expansions of Horn’s hypergeometric function H3 ratios, Mathematics, 9 (2) (2021), Article ID: 148.
  • T. Antonova, R. Dmytryshyn and R. Kurka: Approximation for the ratios of the confluent hypergeometric function Φ(N)D by the branched continued fractions, Axioms, 11 (9) (2022), Article ID: 426.
  • T. Antonova, R. Dmytryshyn and S. Sharyn: Branched continued fraction representations of ratios of Horn’s confluent function H6, Constr. Math. Anal., 6 (1) (2023), 22–37.
  • T. M. Antonova: On convergence of branched continued fraction expansions of Horn’s hypergeometric function H3 ratios, Carpathian Math. Publ., 13 (3) (2021), 642–650.
  • T. Antonova: On structure of branched continued fractions, Carpathian Math. Publ., 16 (2) (2024), 391–400.
  • Z. e. a. Bentalha: Representation of the Coulomb matrix elements by means of Appell hypergeometric function F2, Math. Phys. Anal. Geom., 21 (2018), Article ID: 10.
  • D. I. Bodnar, O. S. Bodnar and I. B. Bilanyk: A truncation error bound for branched continued fractions of the special form on subsets of angular domains, Carpathian Math. Publ., 15 (2) (2023), 437–448.
  • D. I. Bodnar, I. B. Bilanyk: Two-dimensional generalization of the Thron-Jones theorem on the parabolic domains of convergence of continued fractions, Ukr. Math. J., 74 (9) (2023), 1317–1333.
  • D. I. Bodnar: Branched Continued Fractions, Naukova Dumka, Kyiv (1986). (In Russian)
  • D. I. Bodnar: Expansion of a ratio of hypergeometric functions of two variables in branching continued fractions, J. Math. Sci., 64 (32) (1993), 1155–1158.
  • D. I. Bodnar, O. S. Manzii: Expansion of the ratio of Appel hypergeometric functions F3 into a branching continued fraction and its limit behavior, J. Math. Sci., 107 (1) (2001), 3550–3554.
  • D. I. Bodnar: Multidimensional C-fractions, J. Math. Sci., 90 (5) (1998), 2352–2359.
  • R. Dmytryshyn, C. Cesarano, I.-A. Lutsiv and M. Dmytryshyn: Numerical stability of the branched continued fraction expansion of Horn’s hypergeometric function H4, Mat. Stud., 61 (1) (2024), 51–60.
  • R. Dmytryshyn, V. Goran: On the analytic extension of Lauricella–Saran’s hypergeometric function FK to symmetric domains, Symmetry, 16 (2) (2024), Article ID: 220.
  • R. Dmytryshyn, I.-A. Lutsiv and O. Bodnar: On the domains of convergence of the branched continued fraction expansion of ratio H4(a, d + 1; c, d; z)/H4(a, d + 2; c, d + 1; z), Res. Math., 31 (2) (2023), 19–26.
  • R. Dmytryshyn, I.-A. Lutsiv and M. Dmytryshyn: On the analytic extension of the Horn’s hypergeometric function H4, Carpathian Math. Publ. 16 (1) (2024), 32–39.
  • R. I. Dmytryshyn: The multidimensional generalization of g-fractions and their application, J. Comput. Appl. Math., 164–165 (2004), 265–284.
  • H. Exton: Multiple Hypergeometric Functions and Applications, Halsted Press, Chichester (1976).
  • C. F. Gauss: Disquisitiones generales circa seriem infinitam 1 + αβ/1·γ x + α(α+1)β(β+1)/1·2·γ(γ+1) xx + α(α+1)(α+2)β(β+1)(β+2)/1·2·3·γ(γ+1)(γ+3) x3+etc, In Commentationes Societatis Regiae Scientiarum Gottingensis Recentiores, Classis Mathematicae (1812), H. Dieterich: Gottingae, Germany, 2 (1813), 3–46.
  • V. R. Hladun, D. I. Bodnar and R. S. Rusyn: Convergence sets and relative stability to perturbations of a branched continued fraction with positive elements, Carpathian Math. Publ., 16 (1) (2024), 16–31.
  • V. R. Hladun, N. P. Hoyenko, O. S. Manzij and L. Ventyk: On convergence of function F4(1, 2; 2, 2; z1, z2) expansion into a branched continued fraction, Math. Model. Comput., 9 (3) (2022), 767–778.
  • V. Hladun, R. Rusyn and M. Dmytryshyn: On the analytic extension of three ratios of Horn’s confluent hypergeometric function H7, Res. Math., 32 (1) (2024), 60–70.
  • J. Horn: Hypergeometrische Funktionen zweier Veränderlichen, Math. Ann., 105 (1931), 381–407.
  • N. Hoyenko, V. Hladun and O. Manzij: On the infinite remains of the Nórlund branched continued fraction for Appell hypergeometric functions, Carpathian Math. Publ., 6 (1) (2014), 11–25. (In Ukrainian)
  • B. Kol, R. Shir: The propagator seagull: general evaluation of a two loop diagram, J. High Energy Phys., 2019 (2019), Article ID: 83.
  • I. Kovalyov: Rational generalized Stieltjes functions, Constr. Math. Anal., 5 (3) (2022), 154–167.
  • N. Ortner, P, Wagner: On the singular values of the incomplete Beta function, Constr. Math. Anal., 5 (2) (2022), 93–104.
  • M. Pétréolle, A. D. Sokal and B. X. Zhu: Lattice paths and branched continued fractions: An infinite sequence of generalizations of the Stieltjes-Rogers and Thron-Rogers polynomials, with coefficientwise Hankel-total positivity, arXiv, (2020), arXiv:1807.03271v2.
  • J. B. Seaborn: Hypergeometric Functions and Their Applications, Springer, New York (1991).
  • B. V. Shabat: Introduce to complex analysis. Part II. Functions of several variables, American Mathematical Society, Providence (1992).
  • V. S. Vladimirov: Methods of the theory of functions of many complex variables, The MIT Press, Cambridge (1966).
  • H. S. Wall: Analytic Theory of Continued Fractions, D. Van Nostrand Co., New York (1948).

On the analytic extension of the Horn's confluent function $\mathrm{H}_6$ on domain in the space $\mathbb{C}^2$

Yıl 2024, , 11 - 26, 16.12.2024
https://doi.org/10.33205/cma.1545452

Öz

The paper considers the problem of representation and extension of Horn's confluent functions by a special family of functions - branched continued fractions. In a new region, an estimate of the rate of convergence for branched continued fraction expansions of the ratios of Horn's confluent functions $\mathrm{H}_6$ with real parameters is established. Here, region is a domain (open connected set) together with all, part or none of its boundary. Also, a new domain of the analytical continuation of the above-mentioned ratios is established, using their branched continued fraction expansions whose elements are polynomials in the space $\mathbb{C}^2$. These expansions can be used to approximate the solutions of certain differential equations and analytic functions, which are represented by the Horn's confluent functions $\mathrm{H}_6.$

Kaynakça

  • T. Antonova, C. Cesarano, R. Dmytryshyn and S. Sharyn: An approximation to Appell’s hypergeometric function F2 by branched continued fraction, Dolomites Res. Notes Approx., 17 (1) (2024), 22–31.
  • T. Antonova, R. Dmytryshyn and V. Goran: On the analytic continuation of Lauricella-Saran hypergeometric function FK(a1, a2, b1, b2; a1, b2, c3; z), Mathematics, 11 (21) (2023), Article ID: 4487.
  • T. Antonova, R. Dmytryshyn and V. Kravtsiv: Branched continued fraction expansions of Horn’s hypergeometric function H3 ratios, Mathematics, 9 (2) (2021), Article ID: 148.
  • T. Antonova, R. Dmytryshyn and R. Kurka: Approximation for the ratios of the confluent hypergeometric function Φ(N)D by the branched continued fractions, Axioms, 11 (9) (2022), Article ID: 426.
  • T. Antonova, R. Dmytryshyn and S. Sharyn: Branched continued fraction representations of ratios of Horn’s confluent function H6, Constr. Math. Anal., 6 (1) (2023), 22–37.
  • T. M. Antonova: On convergence of branched continued fraction expansions of Horn’s hypergeometric function H3 ratios, Carpathian Math. Publ., 13 (3) (2021), 642–650.
  • T. Antonova: On structure of branched continued fractions, Carpathian Math. Publ., 16 (2) (2024), 391–400.
  • Z. e. a. Bentalha: Representation of the Coulomb matrix elements by means of Appell hypergeometric function F2, Math. Phys. Anal. Geom., 21 (2018), Article ID: 10.
  • D. I. Bodnar, O. S. Bodnar and I. B. Bilanyk: A truncation error bound for branched continued fractions of the special form on subsets of angular domains, Carpathian Math. Publ., 15 (2) (2023), 437–448.
  • D. I. Bodnar, I. B. Bilanyk: Two-dimensional generalization of the Thron-Jones theorem on the parabolic domains of convergence of continued fractions, Ukr. Math. J., 74 (9) (2023), 1317–1333.
  • D. I. Bodnar: Branched Continued Fractions, Naukova Dumka, Kyiv (1986). (In Russian)
  • D. I. Bodnar: Expansion of a ratio of hypergeometric functions of two variables in branching continued fractions, J. Math. Sci., 64 (32) (1993), 1155–1158.
  • D. I. Bodnar, O. S. Manzii: Expansion of the ratio of Appel hypergeometric functions F3 into a branching continued fraction and its limit behavior, J. Math. Sci., 107 (1) (2001), 3550–3554.
  • D. I. Bodnar: Multidimensional C-fractions, J. Math. Sci., 90 (5) (1998), 2352–2359.
  • R. Dmytryshyn, C. Cesarano, I.-A. Lutsiv and M. Dmytryshyn: Numerical stability of the branched continued fraction expansion of Horn’s hypergeometric function H4, Mat. Stud., 61 (1) (2024), 51–60.
  • R. Dmytryshyn, V. Goran: On the analytic extension of Lauricella–Saran’s hypergeometric function FK to symmetric domains, Symmetry, 16 (2) (2024), Article ID: 220.
  • R. Dmytryshyn, I.-A. Lutsiv and O. Bodnar: On the domains of convergence of the branched continued fraction expansion of ratio H4(a, d + 1; c, d; z)/H4(a, d + 2; c, d + 1; z), Res. Math., 31 (2) (2023), 19–26.
  • R. Dmytryshyn, I.-A. Lutsiv and M. Dmytryshyn: On the analytic extension of the Horn’s hypergeometric function H4, Carpathian Math. Publ. 16 (1) (2024), 32–39.
  • R. I. Dmytryshyn: The multidimensional generalization of g-fractions and their application, J. Comput. Appl. Math., 164–165 (2004), 265–284.
  • H. Exton: Multiple Hypergeometric Functions and Applications, Halsted Press, Chichester (1976).
  • C. F. Gauss: Disquisitiones generales circa seriem infinitam 1 + αβ/1·γ x + α(α+1)β(β+1)/1·2·γ(γ+1) xx + α(α+1)(α+2)β(β+1)(β+2)/1·2·3·γ(γ+1)(γ+3) x3+etc, In Commentationes Societatis Regiae Scientiarum Gottingensis Recentiores, Classis Mathematicae (1812), H. Dieterich: Gottingae, Germany, 2 (1813), 3–46.
  • V. R. Hladun, D. I. Bodnar and R. S. Rusyn: Convergence sets and relative stability to perturbations of a branched continued fraction with positive elements, Carpathian Math. Publ., 16 (1) (2024), 16–31.
  • V. R. Hladun, N. P. Hoyenko, O. S. Manzij and L. Ventyk: On convergence of function F4(1, 2; 2, 2; z1, z2) expansion into a branched continued fraction, Math. Model. Comput., 9 (3) (2022), 767–778.
  • V. Hladun, R. Rusyn and M. Dmytryshyn: On the analytic extension of three ratios of Horn’s confluent hypergeometric function H7, Res. Math., 32 (1) (2024), 60–70.
  • J. Horn: Hypergeometrische Funktionen zweier Veränderlichen, Math. Ann., 105 (1931), 381–407.
  • N. Hoyenko, V. Hladun and O. Manzij: On the infinite remains of the Nórlund branched continued fraction for Appell hypergeometric functions, Carpathian Math. Publ., 6 (1) (2014), 11–25. (In Ukrainian)
  • B. Kol, R. Shir: The propagator seagull: general evaluation of a two loop diagram, J. High Energy Phys., 2019 (2019), Article ID: 83.
  • I. Kovalyov: Rational generalized Stieltjes functions, Constr. Math. Anal., 5 (3) (2022), 154–167.
  • N. Ortner, P, Wagner: On the singular values of the incomplete Beta function, Constr. Math. Anal., 5 (2) (2022), 93–104.
  • M. Pétréolle, A. D. Sokal and B. X. Zhu: Lattice paths and branched continued fractions: An infinite sequence of generalizations of the Stieltjes-Rogers and Thron-Rogers polynomials, with coefficientwise Hankel-total positivity, arXiv, (2020), arXiv:1807.03271v2.
  • J. B. Seaborn: Hypergeometric Functions and Their Applications, Springer, New York (1991).
  • B. V. Shabat: Introduce to complex analysis. Part II. Functions of several variables, American Mathematical Society, Providence (1992).
  • V. S. Vladimirov: Methods of the theory of functions of many complex variables, The MIT Press, Cambridge (1966).
  • H. S. Wall: Analytic Theory of Continued Fractions, D. Van Nostrand Co., New York (1948).
Toplam 34 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematiksel Yöntemler ve Özel Fonksiyonlar, Yaklaşım Teorisi ve Asimptotik Yöntemler
Bölüm Makaleler
Yazarlar

Roman Dmytryshyn 0000-0003-2845-0137

Tamara Antonova 0000-0002-0358-4641

Marta Dmytryshyn 0000-0002-0609-9764

Erken Görünüm Tarihi 16 Aralık 2024
Yayımlanma Tarihi 16 Aralık 2024
Gönderilme Tarihi 8 Eylül 2024
Kabul Tarihi 2 Ekim 2024
Yayımlandığı Sayı Yıl 2024

Kaynak Göster

APA Dmytryshyn, R., Antonova, T., & Dmytryshyn, M. (2024). On the analytic extension of the Horn’s confluent function $\mathrm{H}_6$ on domain in the space $\mathbb{C}^2$. Constructive Mathematical Analysis, 7(Special Issue: AT&A), 11-26. https://doi.org/10.33205/cma.1545452
AMA Dmytryshyn R, Antonova T, Dmytryshyn M. On the analytic extension of the Horn’s confluent function $\mathrm{H}_6$ on domain in the space $\mathbb{C}^2$. CMA. Aralık 2024;7(Special Issue: AT&A):11-26. doi:10.33205/cma.1545452
Chicago Dmytryshyn, Roman, Tamara Antonova, ve Marta Dmytryshyn. “On the Analytic Extension of the Horn’s Confluent Function $\mathrm{H}_6$ on Domain in the Space $\mathbb{C}^2$”. Constructive Mathematical Analysis 7, sy. Special Issue: AT&A (Aralık 2024): 11-26. https://doi.org/10.33205/cma.1545452.
EndNote Dmytryshyn R, Antonova T, Dmytryshyn M (01 Aralık 2024) On the analytic extension of the Horn’s confluent function $\mathrm{H}_6$ on domain in the space $\mathbb{C}^2$. Constructive Mathematical Analysis 7 Special Issue: AT&A 11–26.
IEEE R. Dmytryshyn, T. Antonova, ve M. Dmytryshyn, “On the analytic extension of the Horn’s confluent function $\mathrm{H}_6$ on domain in the space $\mathbb{C}^2$”, CMA, c. 7, sy. Special Issue: AT&A, ss. 11–26, 2024, doi: 10.33205/cma.1545452.
ISNAD Dmytryshyn, Roman vd. “On the Analytic Extension of the Horn’s Confluent Function $\mathrm{H}_6$ on Domain in the Space $\mathbb{C}^2$”. Constructive Mathematical Analysis 7/Special Issue: AT&A (Aralık 2024), 11-26. https://doi.org/10.33205/cma.1545452.
JAMA Dmytryshyn R, Antonova T, Dmytryshyn M. On the analytic extension of the Horn’s confluent function $\mathrm{H}_6$ on domain in the space $\mathbb{C}^2$. CMA. 2024;7:11–26.
MLA Dmytryshyn, Roman vd. “On the Analytic Extension of the Horn’s Confluent Function $\mathrm{H}_6$ on Domain in the Space $\mathbb{C}^2$”. Constructive Mathematical Analysis, c. 7, sy. Special Issue: AT&A, 2024, ss. 11-26, doi:10.33205/cma.1545452.
Vancouver Dmytryshyn R, Antonova T, Dmytryshyn M. On the analytic extension of the Horn’s confluent function $\mathrm{H}_6$ on domain in the space $\mathbb{C}^2$. CMA. 2024;7(Special Issue: AT&A):11-26.