I am struggling to store a function without it being evaluated so the function can be differentiated later.

This is my code:

function res = tayexp(x,a,n)
if x <= 0
    error ("x is not within the domain")
elseif isinteger(n) == 0 && sign(n) <= 0
    error ("n must be a positive integer")
elseif sign(a) <= 0
    error ("a cannot be less than or equal to zero")
else
    fd=[];
    f2 = [];
    startfunc(t) = 1./t + log(t)
    for i = (0:1:n-1)
        newfunc = diff(startfunc(), i+1);
        fd = [fd, subs(newfunc,t,x)];
        f2 = [f2, (fd(i+1)*(a)*((x-a)^i)) / factorial(i)];
    end
    res = sum(f2, "all");
end
%goal: make an array of each derivative to the nth degree for 1/x + log(x)
%from there, evaluate each element at x to make an array of numbers
%then plug each value into the taylor series

My issue is that startfunc insists on being evaluated, leading to an error with t which is just an independent variable without a given value.

I have tried nested functions, i have tried making t an empty array, i have tried the @(t) syntax, and none of it seems to work. Any help would be greatly appreciated.

Answer 1

[Steven Lord]

The correct syntax to make that into an anonymous function is:

startfunc = @(t) 1./t + log(t)

startfunc = function_handle with value:
    @(t)1./t+log(t)

Then evaluating it works like:

y = startfunc(1:5)

y = 1×5

1.0000 1.1931 1.4319 1.6363 1.8094

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[Walter Roberson]

newfunc = diff(startfunc(), i+1);

will need to be changed to

syms t
newfunc = diff(startfunc(t), i+1);

[Jaden]

Hello! Using your suggestions, a lot of googling, and some ai, I managed to get the code to run! Thanks for the help, hopefully I won't need more help with additions to this code.