/sci/ - Science & Math

>>12170928
It's the Pade approximation (the 3,3 one).

Take a function f and compute the two polynomials p, q of degree n, m making
p(x)⋅f(x) - q(x)
as close to zero as possible in some sense or on some subset.

If p(x)=1, this is just the Taylor series. In either case, q(x)/p(x)≈f(x).

>>12171306
It expands as x^k/k! up to n=4, followed by alternating terms.
So around x=0it can't be very wrong anyway.

>>12170928
It's the Pade approximation (the 3,3 one).

Take a function [math]f[/math] and compute the two polynomials p, q of degree n, m making
[math]p(x)\cdot f(x)=q(x)[/math]
as close to zero as possible in some sense or on some subset.

If [math]p(x)=1[/math], this is just the Taylor series. In either case, [math]\frac{p(x)}{q(x)}\approx f(x)[/math].

>>12171306
It expands as [math] \sum_{k=0}^n \frac{1}{k!} x^k [/math] where [math] n=4 [/math], followed by alternating terms.
So around [math]x=0 [/math]it can't be very wrong anyway.