Results 11 to 20 of about 1,656,816 (274)

Branched Continued Fraction Expansions of Horn’s Hypergeometric Function H₃ Ratios

Mathematics, 2021
The paper deals with the problem of construction and investigation of branched continued fraction expansions of special functions of several variables. We give some recurrence relations of Horn hypergeometric functions H3. By these relations the branched
Tamara Antonova, Roman Dmytryshyn, Victoriia Kravtsiv   +2 more
doaj   +2 more sources

On branched continued fraction expansions of hypergeometric functions \(F_M\) and their ratios [PDF]

Modern Mathematical Methods
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.
Ivan Nyzhnyk, Roman Dmytryshyn, Tamara Antonova   +2 more
doaj   +3 more sources

On Some Branched Continued Fraction Expansions for Horn’s Hypergeometric Function H₄(a,b;c,d;z₁,z₂) Ratios

Axioms, 2023
The paper deals with the problem of representation of Horn’s hypergeometric functions by branched continued fractions. The formal branched continued fraction expansions for three different Horn’s hypergeometric function H4 ratios are constructed.
Tamara Antonova, Roman Dmytryshyn, Ilona-Anna Lutsiv, Serhii Sharyn   +3 more
doaj   +2 more sources

Generalized Hypergeometric Function ₃F₂ Ratios and Branched Continued Fraction Expansions

Axioms, 2021
The paper is related to the classical problem of the rational approximation of analytic functions of one or several variables, particulary the issues that arise in the construction and studying of continued fraction expansions and their multidimensional ...
Tamara Antonova, Roman Dmytryshyn, Serhii Sharyn   +2 more
doaj   +2 more sources

On the branched continued fraction expansions of the complete group of ratios of the generalized hypergeometric function $_4F_3$ [PDF]

Researches in Mathematics
The paper considers the classical problem of the rational approximation of analytic functions of complex variable, in particulary, to issues that arise when constructing branched continued fraction expansions for generalized hypergeometric functions ...
Y. Lutsiv, T. Antonova, R. Dmytryshyn, M. Dmytryshyn   +3 more
doaj   +2 more sources

Intrapatient tumour heterogeneity and clonal evolution in an autopsy study of metastatic salivary gland cancer. [PDF]

Mol Oncol
Tumour heterogeneity and clonal evolution of metastatic salivary gland cancer were evaluated in two patients with adenoid carcinoma and one patient with myoepithelial carcinoma. Radiology‐guided autopsy enabled multi‐region sampling (total samples n = 149), followed by whole‐genome sequencing and phylogenetic reconstruction (17 tumour samples, 4–7 per ...
Lassche G, van Ruitenbeek NJ, Adang C, O'Gorman L, Lee PY, Klein WM, van Engen-van Grunsven ACH, Schalken JA, Bervoets S, Verhaegh GW, van Herpen CML.   +10 more
europepmc   +2 more sources

Approximation of functions of several variables by multidimensional $S$-fractions with independent variables

Karpatsʹkì Matematičnì Publìkacìï, 2021
The paper deals with the problem of approximation of functions of several variables by branched continued fractions. We study the correspondence between formal multiple power series and the so-called "multidimensional $S$-fraction with independent ...
R.I. Dmytryshyn, S.V. Sharyn
doaj   +1 more source

Some convergence regions of branched continued fractions of special form

Karpatsʹkì Matematičnì Publìkacìï, 2013
Some circular and parabolic convergence regions for branched continued fractions of special form are established.
O.E. Baran
doaj   +3 more sources

On the domains of convergence of the branched continued fraction expansion of ratio $H_4(a,d+1;c,d;\mathbf{z})/H_4(a,d+2;c,d+1;\mathbf{z})$

Researches in Mathematics, 2023
The paper considers the problem of establishing the convergence criteria of the branched continued fraction expansion of the ratio of Horn's hypergeometric functions $H_4$. To solve it, the technique of expanding the domain of convergence of the branched
R.I. Dmytryshyn, I.-A.V. Lutsiv, O.S. Bodnar   +2 more
doaj   +1 more source

Three- and four-term recurrence relations for Horn's hypergeometric function $H_4$

Researches in Mathematics, 2022
Three- and four-term recurrence relations for hypergeometric functions of the second order (such as hypergeometric functions of Appell, Horn, etc.) are the starting point for constructing branched continued fraction expansions of the ratios of these ...
R.I. Dmytryshyn, I.-A.V. Lutsiv
doaj   +1 more source