How can I define the error function and use a Maclaurin series to approximate a value?

My question is: erf (x) = 2/sqrt(pi)*integral(exp(-(t^2)) from 0 to x

(a) Use the Maclaurin series (Taylor series centered at 0) to construct a table for erf (x) that is accurate

to 10^-4 for erf (xi) where xi = 0:2i for i = 0; 1; : : : ; 5.

I first defined the function and then realized that erf is a built in function so I tried

erf = @(x) erf(x)

erf = function_handle with value:
    @(x)erf(x)

but got this response:

Unable to find function@(x)(2/(sqrt(pi)))*integral(exp(-(t^2)),0,x) within

C:\Users\dboeh\OneDrive\Documents\NAU\MAT 362\dbb223_03.m.

Does anyone have ideas?

Answer 1

[Sam Chak]

Hi @codeconstructo

Are you looking for something like this?

syms x
T1 = taylor(erf(x))

T1 = 

[codeconstructo]

When I try that i get the response Unable to find function @(x)erf(x)

[codeconstructo]

@Sam Chak

[Sam Chak]

Hi @codeconstructo

The built-in erf() function is stored in MATLAB installation directory.

which erf

built-in (/MATLAB/toolbox/matlab/specfun/@double/erf)  % double method

You created an anonymous function in a m-file script (dbb223_03.m) which has the same filename as the built-in one and ran the m-file in OneDrive. So, it tries to search erf within the m-file. Try assigning another name.

% Creating an anonymous function
anonfcn = @(x) erf(x)

anonfcn = function_handle with value:
    @(x)erf(x)

% Built-in
erf(pi)

ans = 1.0000

% Test
anonfcn(pi)

ans = 1.0000