Results 1 to 10 of about 323 (166)

Solutions of complex nonlinear functional equations including second order partial differential and difference in C^2

Electronic Journal of Differential Equations, 2023
This article is devoted to exploring the existence and the form of finite order transcendental entire solutions of Fermat-type second order partial differential-difference equations $$ \Big(\frac{\partial^2 f}{\partial z_1^2}+\delta\frac{\partial^2 f ...
Hong Yan Xu, Goutam Haldar
doaj   +3 more sources

L-Index in Joint Variables: Sum and Composition of an Entire Function with a Function With a Vanished Gradient

Fractal and Fractional, 2023
The composition H(z)=f(Φ(z)) is studied, where f is an entire function of a single complex variable and Φ is an entire function of n complex variables with a vanished gradient.
Andriy Bandura, Tetyana Salo, Oleh Skaskiv   +2 more
doaj   +1 more source

Representation of Some Ratios of Horn’s Hypergeometric Functions H₇ by Continued Fractions

Axioms, 2023
The paper deals with the problem of representation of Horn’s hypergeometric functions via continued fractions and branched continued fractions. We construct the formal continued fraction expansions for three ratios of Horn’s hypergeometric functions H7 ...
Tamara Antonova, Roman Dmytryshyn, Pavlo Kril, Serhii Sharyn   +3 more
doaj   +1 more source

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   +1 more source

On the Analytic Continuation of Lauricella–Saran Hypergeometric Function F_K(a₁,a₂,b₁,b₂;a₁,b₂,c₃;z)

Mathematics, 2023
The paper establishes an analytical extension of two ratios of Lauricella–Saran hypergeometric functions FK with some parameter values to the corresponding branched continued fractions in their domain of convergence.
Tamara Antonova, Roman Dmytryshyn, Vitaliy Goran   +2 more
doaj   +1 more source

Characterizations of entire solutions for the system of Fermat-type binomial and trinomial shift equations in ℂn#

Demonstratio Mathematica, 2023
In this article, we investigate the existence and the precise form of finite-order transcendental entire solutions of some system of Fermat-type quadratic binomial and trinomial shift equations in Cn{{\mathbb{C}}}^{n}. Our results are the generalizations
Haldar Goutam, Banerjee Abhijit
doaj   +1 more source

$L^2$ extension theorem for jets with variable denominators

Comptes Rendus. Mathématique, 2021
By studying the variable denominators introduced by X. Zhou–L. Zhu, we generalize the results of D. Popovici for the $L^2$ extension theorem for jets. As a direct corollary, we also give a generalization of T. Ohsawa–K. Takegoshi’s extension theorem to a
Rao, Sheng, Zhang, Runze
doaj   +1 more source

Extension Theorem for Complex Clifford Algebras-Valued Functions on Fractal Domains

Boundary Value Problems, 2010
Monogenic extension theorem of complex Clifford algebras-valued functions over a bounded domain with fractal boundary is obtained. The paper is dealing with the class of Hölder continuous functions.
Paul Bosch, Ricardo Abreu-Blaya, Juan Bory-Reyes   +2 more
doaj   +2 more sources

ON CERTAIN SUB-SPACE OF X

مجلة بغداد للعلوم, 2008
The study of properties of space of entire functions of several complex variables was initiated by Kamthan [4] using the topological properties of the space. We have introduced in this paper the sub-space of space of entire functions of several complex
Baghdad Science Journal
doaj   +1 more source

Exact forms of entire solutions for Fermat type partial differential equations in C^2

Electronic Journal of Differential Equations, 2021
This article studies the existence and the exact form of entire solutions of several Fermat type partial differential equations in \(\mathbb{C}^2\), by utilizing the Nevanlinna theory of meromorphic functions in several complex  variables.
Yu Xian Chen, Hong Yan Xu
doaj   +1 more source