Exact BDF stability angles with maple

BDF formulas are among the most efficient methods for numerical integration, in particular of stiff equations (see e.g. Gear in Numerical initial value problems in ordinary differential equations, Prentice Hall, Upper Saddle River, 1971). Their excellent stability properties are known for precisely half a century, from the first calculation of their angles of A(α ) -stability by Nørsett (BIT, 9:259–263, 1969). Later, more insight was gained and more precise values were calculated numerically (see for example Hairer and Wanner in Solving ordinary differential equations, Springer, New York, 1996, Sect. V.2). This was the state-of-the-art, when Akrivis and Katsoprinakis (BIT, 2019. https://doi.org/10.1007/s10543-019-00768-1 ) discovered exact values for these angles. In this note we simplify the derivation and results by using Maple.