Timeline for Constructing a linear ODE for a product of two holonomic functions without introducing additional singularities
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 31, 2013 at 13:47 | comment | added | Alexandre Eremenko | The paper is about entire solutions. The singular point is at infinity. They prove that the class of solutions of linear differential equations with polynomial coefficients and NO singular points in C (that is the top coefficient is 1) is an algebra. That is this class of functions is closed under addition and multiplication. This is a special case of your conjecture. They also say that if you consider entire coefficients (not necessarily polynomials) the class of solutions you obtain is not even closed with respect to addition. | |
| Mar 31, 2013 at 12:48 | comment | added | dima | Since my German is nonexistent, could you please pinpoint the location in the paper where they talk about the case of one singular point? Also, I couldn't figure out if they always assume that the solutions of the ODEs are entire functions... | |
| Mar 29, 2013 at 13:00 | history | answered | Alexandre Eremenko | CC BY-SA 3.0 |