Finding Hyperexponential Solutions of Differential Equations
Sprache des Vortragstitels:
Englisch
Original Tagungtitel:
nvited talk at Siam Conference on Applied Algebraic Geometry
Sprache des Tagungstitel:
Englisch
Original Kurzfassung:
We consider ordinary linear differential equations with polynomial coefficients. Each such equation has a finite dimensional vector space of solutions, but usually none of these solutions can be expressed in closed form. We discuss the problem of finding out for a given differential equation whether one (or some, or all) of its solutions admit a closed form. We focus on hyperexponential solutions. These are solutions that can be written in the form exp(u(x))v_1(x)^{e_1}... v_k(x)^{e_k} for certain rational functions u,v_1,...,v_k and constants e_1,... ,e_k. There is a classical algorithm for finding solutions of this form, but it is very expensive. We present a more efficient algorithm, published a few weeks ago at ISSAC'13.
Sprache der Kurzfassung:
Englisch
Vortragstyp:
Hauptvortrag / Eingeladener Vortrag auf einer Tagung
Forschungs-