# Latest Posts

Last edited: 2020-12-31 16:16:20

When I was young, I was curious to know how a computer calculates functions such as the cosine, the logarithm, or the tangent's inverse, the so-called elementary transcendental functions.

It turns out that they are calculated with the so-called *Chebyshev* polynomial approximation, where you get each polynomial coefficient by solving an integral.

In some cases, you need a couple of tens of coefficients, so there are lots of integrals to solve. It is more complicated when the function you want to approximate appears in those integrals, because you don't have how to calculate that function yet, and that's precisely why you want to have the approximation!

With patience and a little luck, I could analytically solve the approximation to some of these functions; and here I will tell you how I did it.

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