A Study of Certain Special Cases of the Hypergeometric Differential Equation

1892 ◽  
Vol 7 (1/5) ◽  
pp. 145
Author(s):  
James Harrington Boyd
Keyword(s):  
Differential Equation ◽  
Hypergeometric Differential Equation ◽  
Special Cases

scholarly journals A Convergent Collocation Approach for Generalized Fractional Integro-Differential Equations Using Jacobi Poly-Fractonomials

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 979
Author(s):  
Sandeep Kumar ◽  
Rajesh K. Pandey ◽  
H. M. Srivastava ◽  
G. N. Singh
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Collocation Method ◽  
Caputo Fractional Derivative ◽  
Fractional Derivatives ◽  
Special Cases ◽  
Collocation Approach ◽  
Linear And Nonlinear ◽  
Simulation Results ◽  
Theoretical Results

In this paper, we present a convergent collocation method with which to find the numerical solution of a generalized fractional integro-differential equation (GFIDE). The presented approach is based on the collocation method using Jacobi poly-fractonomials. The GFIDE is defined in terms of the B-operator introduced recently, and it reduces to Caputo fractional derivative and other fractional derivatives in special cases. The convergence and error analysis of the proposed method are also established. Linear and nonlinear cases of the considered GFIDEs are numerically solved and simulation results are presented to validate the theoretical results.

scholarly journals k-Hypergeometric Series Solutions to One Type of Non-Homogeneous k-Hypergeometric Equations

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 262 ◽  
Author(s):  
Shengfeng Li ◽  
Yi Dong
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Hypergeometric Series ◽  
Second Order ◽  
Series Solutions ◽  
Frobenius Method ◽  
General Solutions ◽  
Hypergeometric Differential Equation ◽  
Polynomial Term ◽  
Hypergeometric Equations

In this paper, we expound on the hypergeometric series solutions for the second-order non-homogeneous k-hypergeometric differential equation with the polynomial term. The general solutions of this equation are obtained in the form of k-hypergeometric series based on the Frobenius method. Lastly, we employ the result of the theorem to find the solutions of several non-homogeneous k-hypergeometric differential equations.

scholarly journals THE GENERALIZED MATRIX VALUED HYPERGEOMETRIC EQUATION

2010 ◽  
Vol 21 (02) ◽  
pp. 145-155 ◽  
Author(s):  
P. ROMÁN ◽  
S. SIMONDI
Keyword(s):  
Differential Equation ◽  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Hypergeometric Functions ◽  
Spherical Functions ◽  
Hypergeometric Equation ◽  
Necessary Condition ◽  
Hypergeometric Differential Equation ◽  
The Matrix ◽  
Generalized Matrix

The matrix valued analog of the Euler's hypergeometric differential equation was introduced by Tirao in [4]. This equation arises in the study of matrix valued spherical functions and in the theory of matrix valued orthogonal polynomials. The goal of this paper is to extend naturally the number of parameters of Tirao's equation in order to get a generalized matrix valued hypergeometric equation. We take advantage of the tools and strategies developed in [4] to identify the corresponding matrix hypergeometric functions nFm. We prove that, if n = m + 1, these functions are analytic for |z| < 1 and we give a necessary condition for the convergence on the unit circle |z| = 1.

The Out-of-Plane Stability Analysis of Crane Jib with Two Symmetric Drawbars

2013 ◽  
Vol 446-447 ◽  
pp. 469-473
Author(s):  
Nian Li Lu ◽  
Ce Chen ◽  
Shi Ming Liu
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Boundary Conditions ◽  
Characteristic Equation ◽  
Critical Condition ◽  
Design Rules ◽  
Special Cases ◽  
Out Of Plane

The out-of-plane stability of the crane jib with two symmetric drawbars is studied. Differential equation with two non-conservative forces caused by the two symmetric drawbars is established in critical condition. According to the boundary conditions and proper parameter processing, the out-of-plane characteristic equation is obtained for the crane jib. Comparison with the ANSYS results verified the correctness of the method. And special cases are given to show the consistency of the method used in this paper and that with one drawbar given by the Chinese Design Rules for crane (GB3811-2008). The contribution of the angle between two symmetric drawbars to the out-of-plane stability of the crane jib is also discussed. The results show that, the crane jib with two symmetric drawbars has higher out-of-plane stability than that with one drawbar, and the increase of the angle between the two symmetric drawbars will lead to the significant increase of the out-of-plane stability of the crane jib.

Hypergeometric Differential Equation

1991 ◽  
pp. 25-116
Author(s):  
Katsunori Iwasaki ◽  
Hironobu Kimura ◽  
Shun Shimomura ◽  
Masaaki Yoshida
Keyword(s):  
Differential Equation ◽  
Hypergeometric Differential Equation

scholarly journals Affine Schwarz Map for the Hypergeometric Differential Equation

2008 ◽  
Vol 51 (2) ◽  
pp. 281-305 ◽  
Author(s):  
Ryoichi Kobayashi ◽  
Tatsuya Nishizaka ◽  
Shoji Shinzato ◽  
Masaaki Yoshida
Keyword(s):  
Differential Equation ◽  
Hypergeometric Differential Equation

The integral of geometric Brownian motion

2001 ◽  
Vol 33 (1) ◽  
pp. 223-241 ◽  
Author(s):  
Daniel Dufresne
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Brownian Motion ◽  
Laplace Transform ◽  
Finite Time ◽  
Geometric Brownian Motion ◽  
Time Interval ◽  
Finite Time Interval ◽  
Special Cases ◽  
The Laplace Transform

This paper is about the probability law of the integral of geometric Brownian motion over a finite time interval. A partial differential equation is derived for the Laplace transform of the law of the reciprocal integral, and is shown to yield an expression for the density of the distribution. This expression has some advantages over the ones obtained previously, at least when the normalized drift of the Brownian motion is a non-negative integer. Bougerol's identity and a relationship between Brownian motions with opposite drifts may also be seen to be special cases of these results.

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