I created a method for both approximating a function and extending a it's domain from a Natural to a Real Domain. Does this have a name already or any interesting application?(adsbygoogle = window.adsbygoogle || []).push({});

Basically. Add polynomial of degree 0, 1, 2, 3, etc. Making at the same time the approximation function equal to f(0), f(1), f(2), f(3), etc.

The approximation of function f is:

App. of f http://latex.codecogs.com/examples/a0d1659d13fd1904ffe767edc6cab6e4.gif [Broken]

n is level of the approximation, the bigger the n the bigger the approximation and the more the polynomia.

http://latex.codecogs.com/examples/10d3e8addce0f1cea366f3eafcae03df.gif [Broken]=f(n)-App. of f at n of level (n-1)

http://latex.codecogs.com/examples/00d8763b00aac3dd87168ec5039ec758.gif [Broken]

http://latex.codecogs.com/examples/92cf5169e1dbb1a99d49de59187bc652.gif [Broken]

etc.

The idea is actually very simple! Just add a constant and then a line and then a parabola, etc to make it similar to the function.

Also can anyone find a simpler way to find the coefficients. E? Maybe for f(x)=x! ?

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# Does this method have a name? Function Approximation by Polynomial Sum

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