scholarly journals On A Matrix Hypergeometric Differential Equation

2021 ◽  
Vol 20 (1) ◽  
pp. 182-185
Author(s):  
Salah Hamd ◽  
Faisal Saleh Abdalla ◽  
Ahmed Shletiet
Keyword(s):  
Differential Equation ◽  
Hypergeometric Function ◽  
Complex Plane ◽  
Asymptotic Expansions ◽  
Matrix Functions ◽  
Order Linear Differential Equation ◽  
Hypergeometric Differential Equation ◽  
Special Matrix ◽  
Linear Differential ◽  
Special Matrix Functions

In this paper we consider a matrix Hypergeometric differential equation, which are special matrix functions and solution of a specific second order linear differential equation. The aim of this work is to extend a well known theorem on Hypergeometric  function in the complex plane to a matrix version, and we  show that  the asymptotic expansions of  Hypergeometric  function in the complex plane ” that are given in the literature are special members of our main result. Background and motivation are discussed.

On the asymptotic expansions of solutions of an nth order linear differential equation

1980 ◽  
Vol 85 (1-2) ◽  
pp. 15-57 ◽  
Author(s):  
R. B. Paris
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Asymptotic Expansions ◽  
Asymptotic Theory ◽  
Arbitrary Order ◽  
Order Linear Differential Equation ◽  
Linear Ordinary Differential Equations ◽  
Hypergeometric Type ◽  
Independent Variable ◽  
Linear Differential

SynopsisThe asymptotic expansions of solutions of a class of linear ordinary differential equations of arbitrary order n are investigated for large values of the independent variable z in the complex plane. Solutions are expressed in terms of Mellin-Barnes integrals and their asymptotic expansions are subsequently determined by means of the asymptotic theory of integral functions of the hypergeometric type. Three classes of solutions are considered: (i) solutions whose behaviour is either exponentially large or algebraic for |z|→∞ in different sectors of the z-plane, (ii) solutions which are even and odd functions of z when the order n of the differential equation is even and (iii) solutions which are exponentially damped as |z|→∞ in a certain sector of the z-plane.

scholarly journals Solutions ofk-Hypergeometric Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Shahid Mubeen ◽  
Mammona Naz ◽  
Abdur Rehman ◽  
Gauhar Rahman
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Second Order ◽  
Order Linear Differential Equation ◽  
Frobenius Method ◽  
Order Linear ◽  
Hypergeometric Differential Equation ◽  
Linear Differential

We solve the second-order linear differential equation called thek-hypergeometric differential equation by using Frobenius method around all its regular singularities. At each singularity, we find 8 solutions corresponding to the different cases for parameters and modified our solutions accordingly.

scholarly journals Correctness conditions for high-order differential equations with unbounded coefficients

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Kordan N. Ospanov
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Order Linear Differential Equation ◽  
Unbounded Coefficients ◽  
Weighted Norms ◽  
Uniqueness Of The Solution ◽  
Linear Differential

AbstractWe give some sufficient conditions for the existence and uniqueness of the solution of a higher-order linear differential equation with unbounded coefficients in the Hilbert space. We obtain some estimates for the weighted norms of the solution and its derivatives. Using these estimates, we show the conditions for the compactness of some integral operators associated with the resolvent.

A property of the asymptotic series for a class of Titchmarsh–Weyl m-functions

1986 ◽  
Vol 102 (3-4) ◽  
pp. 253-257 ◽  
Author(s):  
B. J. Harris
Keyword(s):  
Differential Equation ◽  
Asymptotic Expansion ◽  
Linear Differential Equation ◽  
Asymptotic Series ◽  
Second Order ◽  
Order Linear Differential Equation ◽  
Order Linear ◽  
The Real ◽  
Linear Differential ◽  
Image Position

SynopsisIn an earlier paper [6] we showed that if q ϵ CN[0, ε) for some ε > 0, then the Titchmarsh–Weyl m(λ) function associated with the second order linear differential equationhas the asymptotic expansionas |A| →∞ in a sector of the form 0 < δ < arg λ < π – δ.We show that if the real valued function q admits the expansionin a neighbourhood of 0, then

scholarly journals A Comparison between the fourth order linear differential equation with its boundary value problem

2020 ◽  
Vol 99 (3) ◽  
pp. 18-25
Author(s):  
Karwan H.F. Jwamer ◽  
◽  
Rando R.Q. Rasul ◽  
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Linear Differential Equation ◽  
Fourth Order ◽  
Upper Bound ◽  
Boundary Value ◽  
Order Linear Differential Equation ◽  
Order Linear ◽  
Linear Differential

In this paper, we study a fourth order linear differential equation. We found an upper bound for the solutions of this differential equation and also, we prove that all the solutions are in L4(0, ∞). By comparing these results we obtain that all the eigenfunction of the boundary value problem generated by this differential equation are bounded and in L4(0, ∞).

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