scholarly journals Reduction of the ordinary linear differential equation of the $n$th order whose coefficients are certain polynomials in a parameter to a system of $n$ first-order equations which are linear in the parameter

1927 ◽  
Vol 29 (3) ◽  
pp. 497-497
Author(s):  
Charles E. Wilder
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Ordinary Linear Differential Equation ◽  
First Order ◽  
Linear Differential

Studies in multiplicative solutions to linear differential equations

1987 ◽  
Vol 106 (3-4) ◽  
pp. 277-305 ◽  
Author(s):  
F. M. Arscott
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Floquet Theory ◽  
Special Functions ◽  
Linear Differential Equations ◽  
Ordinary Linear Differential Equation ◽  
Closed Path ◽  
Starting Point ◽  
Linear Differential

SynopsisGiven an ordinary linear differential equation whose singularities are isolated, a solution is called multiplicative for a closed path C if, when continued analytically along C, it returns to its starting-point merely multiplied by a constant. This paper first classifies such paths into three types, then investigates combinations of two such paths, in which a number of qualitatively different situations can arise. A key result is also given relating to a three-path combination. There are applications to special functions and Floquet theory for periodic equations.

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