Chebishev polynomials, don't know how to use "chebpoly"

I wrote the following code to approximate a 2 variables function:

clear
clc
close all

FlowMeasurements = chebpts(5,[-0.2,0.8]); % mass flow Chebyshev
SpeedMeasurements = chebpts(5,[25000, 55000]);  %Rotational speed Chebyshev

CompressorMapMatrix =[

    1.5805    1.2092    1.1402    1.0234    1.0095
    1.6553    1.2840    1.2564    1.0565    1.0287
    1.9070    1.5357    1.7124    1.2518    1.1505
    2.2873    1.9160    2.4317    1.7374    1.4732
    2.4935    2.1222    2.8189    2.0728    1.7064]; % I put the points Chebishev will ask

FlowVector = -0.2:0.01:0.8;
approximationResult  =  chebfun2(CompressorMapMatrix,[ -0.2 0.8 25000 55000]);
a = chebcoeffs2(approximationResult); %a_ij Matrix

for i=1:length(SpeedMeasurements)  
figure(2)
plot(approximationResult(FlowVector, SpeedMeasurements(i)));
hold on
grid on
end

Now I have to write this equation:

I have the a_ij Matrix, but I don't know how to get the:

I know for sure I have to use chebpoly but I don't know how.

This maybe could help:

https://www.chebfun.org/docs/guide/guide04.html

Answer 1

[Paul Rogers]

maybe this can help

By Chebyshev points we shall mean the set of points in [−1,1] defined by

xj=−cos(jπ/N), 0≤j≤N,

where N≥1 is an integer. (If N=0, we take x0=0.) A fuller name is that these are Chebyshev points of the second kind. (Chebfun also enables computations based on Chebyshev points of the first kind; see Section 8.9.) Through any data values fj at these points there is a unique polynomial interpolant p(x) of degree ≤N, which we call the Chebyshev interpolant. In particular, if the data are fj=(−1)n−j, then p(x) is TN(x), the degree N Chebyshev polynomial, which can also be defined by the formula TN(x)=cos(Ncos−1(x)). In Chebfun, the command chebpoly(N) returns a chebfun corresponding to TN, and poly returns coefficients in the monomial basis 1,x,x2,…. Thus we can print the coefficients of the first few Chebyshev polynomials like this:

taken from here

Answer 2

[Paul Rogers]

Can anyone help me on how to find T_i and T_j?