How do I define this integral function?

Attached is a pdf of the function I am trying to define. t' is the integral variable (which in the code I name x). ω, s, μ are variable parameters that will take a range of values that the user chooses. AT is a vector of 12054 temperatures which, for simplicity, we can consider all values in the vector as 1. My function so far is this:

% Lambda needs to contain all the values for each value of t.
function integral = lamb(s,om,mu,AT)
t = max(s)+1:numel(AT);
for ti = 1:numel(t)
    fun1 = @(x) om.^abs(x-s).*AT(t(ti)-x); % Numerator
    q = @(x) integral(fun1,0,t(ti)); % Integral of the numerator
    fun2 = @(x) om.^abs(x-s); % Denominator
    p = @(x) integral(fun2,0,t(ti)); % Integral of the denominator
    lambda = mu + q/p; % Function seen in pdf 
end

I run this function using this script:

% Here I would load AT but for simplicity let it be vector of 1's.
s = 0:60; % lag range
om = 0.1:0.1:1; % decay rate range
mu = 1:10; % baseline rate range
Ns = numel(s);
Nom = numel(om);
Nmu = numel(mu);
nll = nan(Ns,Nom,Nmu);
for si = 1:Ns
    omi = 1:Nom;
    mui = 1:Nmu;
    integral(si,omi,mui) = lamb(s(si),om(omi),mu(mui),AT);
end

I end up with the error:

Error using  / 
Arguments must be numeric, char, or logical.
% This error is for the final line in the for loop in the function.

If anyone could help me with this function it would be much appreciated, thank you.

Answer 1

[David Goodmanson]

Hello LT,

fun1 = @(x) x.^2
q1 = @(x) integral(fun1,0,4)
q2 = integral(fun1,0,4)

   q1 =  function_handle with value:
         @(x)integral(fun1,0,4)
   
   q2 = 21.3333

I assume that you want a numerical result for q, but the extra @(x) creates a function handle instead.

[Leo Tu]

Thank you @David Goodmanson, that certainly helps!