Quotients of solutions of linear algebraic differential equations
Author: Lee A. Rubel
Journal: Proc. Amer. Math. Soc. 113 (1991), 747-748
MSC: Primary 34A20; Secondary 30D20
MathSciNet review: 1052579
Abstract: An example is given of two entire functions that satisfy linear differential equations with polynomial coefficients, whose quotient is entire, yet satisfies no such differential equation.
-  C. Ward Henson, Lee A. Rubel, and Michael F. Singer, Algebraic properties of the ring of general exponential polynomials, Complex Variables Theory Appl. 13 (1989), no. 1-2, 1–20. MR 1029352, https://doi.org/10.1080/17476938908814374
-  J. F. Ritt, Algebraic combinations of exponentials, Trans. Amer. Math. Soc. 31 (1929), no. 4, 654–679. MR 1501505, https://doi.org/10.1090/S0002-9947-1929-1501505-4