First, I am going to talk about what has been done since last week. I implemented methods to find a recurrence relation in the coefficients of Power series expansion of a Holonomic Function, and then method to find the Power series.
One of the many interesting properties of Holonomic Functions is that the coefficients in Power series expansion of a Holonomic function is a Holonomic sequence, i.e. these coefficients satisfy a recurrence relation having polynomial coefficients.
This recurrence relation can be used to efficiently calculate the coefficients of Power series. The PR 11153 had these methods and got merged today. Here are a couple of examples of the implementation.
In : p = HolonomicFunction(Dx – 1, x, 0, ) # exp(x)
In : p.to_sequence()
Out : HolonomicSequence((-1) + (n + 1)Sn, n), u(0) = 1
In : p.series()
Out : 1 + x + x**2/2 + x**3/6 + x**4/24 + x**5/120 + O(x**6)
For this week it is planned first to implement a method to numerically integrate differential equations of holonomic type from any point
x=b in the complex plane. The next thing to implement after this would probably be converting symbolic functions/expressions to Holonomic Functions.
Cheers and Happy Coding.