Saving intermediate variable values of a recursive function - matlab

Question

I'm trying to code a function calculating difference quotients. I need to this for polynomial interpolation. Given nodes x = linspace(a,b,n+1), function values at the nodes y = func(x) I want to find the values of difference quotients f[x0], f[x_0,x_1], ..., f[x_0,x_1,...,x_n]. To calculate f[x_0,x_1,...,x_n] I will need f[x_0,x_1,...,x_(n-1)], etc., thus it would be a good idea save the intermediate steps on my way to f[x_0,x_1,...,x_n], so that on my way to f[x_0,x_1,...,x_n] I will save the preceding difference quotients as elements of a vector.
Could someone tell me how to correct my code in order to save appropriate difference quotient values? Here's the code:
function [fx, all_fx] = ilo2(a,b,x,y,fx,all_fx)
if a == b
fx(end+1) = y(a);
if a == 1
all_fx(end+1) = fx(end);
end
return
end
a;
b;
[c, all_fx] = ilo2(a+1,b,x,y,fx,all_fx);
[d, all_fx] = ilo2(a,b-1,x,y,fx,all_fx);
fx(end+1) = (c-d)/(b-a);
if a == 1
all_fx(end+1) = fx(end);
end
end
The difference quotients I need are under 'if a == 1' condition.

Answer 1

Ok, I think I fixed it:
function [all_fx,fx] = ilo(a,b,x,y,all_fx,fx)
if a == b
fx(end+1) = y(a);
if a == 1
all_fx(end+1) = fx(end);
end
return
end
[all_fx,c] = ilo(a+1,b,x,y,all_fx,fx);
[all_fx,d] = ilo(a,b-1,x,y,all_fx,fx);
fx(end+1) = (c-d)/(b-a);
if a == 1
all_fx(end+1) = fx(end);
end
end