Yesterday finished with:
Can we expand this further?
Well, applying the product rule
And we know and
Applying L’Hospital’s rule again:
This process can continue – delivering higher order derivatives on each iteration. It even starts to look like we might generate the factoral terms, as now we can see:
- Taylor series expansions and L’Hospital’s rule (cartesianproduct.wordpress.com)
- Euler’s Identity, Part Two [EvolutionBlog] (scienceblogs.com)