The Fourth-Order Type Linear Ordinary Differential Equations

2006/03/21 by Everitt, W. N., Smith, D. J., van Hoeij, M.
#33D15 #33F10. Secondary: 33C05 #34B05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Primary: 33C15

paper · doi:10.48550/arxiv.math/0603516

Abstract

This note reports on the recent advancements in the search for explicit representation, in classical special functions, of the solutions of the fourth-order ordinary differential equations named Bessel-type, Jacobi-type, Laguerre-type, Legendre-type.

Related

• Fourth-order Bessel-type special functions: a survey
• On the higher-order differential equations for the generalized Laguerre polynomials and Bessel functions
• On the inverse problem of calculus of variations
• Solutions for one class of nonlinear fourth-order partial differential equations
• An algebraic approach for solving fourth-order partial differential equations