Table with for loops taylor

Hi

I want to create a table

column 1 will be the value of n from 1 to 20 n= 1, 2, 3, ... , 20

column 2 will be the nth (respectively) taylor approximation of a function [ so n terms of a taylor approximation of ]

column 3 will be the error of this taylor approximation compared to the real value of erf(2) so [erf(2)-nth term taylor approx]

column 4 will be a different series approximation of the same function erf(2) [asymptotic series ] where the double !! means only odd numbers, i.e. .

column 5 will be the error of this second approximation, i.e. [erf(2) minus my n-term asymptotic approximation]

Below is my try. my tayterm doesn't work, neither does my asymterm. The values given are incorrect.

:( thank you.

i would also like gridlines on the table...not sure how to do that.

format long

syms k x t X




%tayt =[taylor(erf(x),x,'Order',2),taylor(erf(x),x,'Order',3),taylor(erf(x),x,'Order',4),taylor(erf(x),x,'Order',5),taylor(erf(x),x,'Order',6),taylor(erf(x),x,'Order',7),taylor(erf(x),x,'Order',8),taylor(erf(x),x,'Order',9),taylor(erf(x),x,'Order',10),taylor(erf(x),x,'Order',11),taylor(erf(x),x,'Order',12),taylor(erf(x),x,'Order',13),taylor(erf(x),x,'Order',14),taylor(erf(x),x,'Order',15),taylor(erf(x),x,'Order',16),taylor(erf(x),x,'Order',17),taylor(erf(x),x,'Order',18),taylor(erf(x),x,'Order',19)];


for n=1:18
    N(n)=n;
    tayterm(n)=taylor(erf(x),x,'Order',n);
    ercol2(n) = erf(2)-tayterm(n);
    asymterm(n)=1-2/sqrt(pi)*exp(-2^2)*(symsum((-1)^k*x^(2*k+1)/((2*k+1)*factorial(k)),k,0,n-1));
    ercol4(n) = erf(2)-asymterm(n);
end
format long
T = table(transpose(N),transpose(double(tayterm)),transpose(ercol2), transpose(asymterm),transpose(ercol4));
    T.Properties.VariableNames = {'n' 'n-term Taylor Approx for erf(2)' 'Error in col 2' 'n-term asymptotic approx of erf(2)' 'Error in col 4'}

[Sindar]

In what way does it not work?

I haven't used symbolic math much, but my first thought is that it doesn't want to create an array. Try cell arrays instead:

tayterm{n}=taylor(2/sqrt(pi)*erf(x),t,0,'Order',n);

[Ursula Trigos-Raczkowski]

it gives me incorrect values for the tayterm and asymterm

the curly brackets give me an error

Error using sym/subsasgn (line 942)

Invalid indexing assignment.

Error in testing (line 7)

tayterm{n}=taylor(2/sqrt(pi)*erf(x),t,0,'Order',n);

[Sindar]

Could be that your function ( erf(x) ) and variable (t) are different, try:

tayterm(n)=taylor(erf(t),t,0,'Order',n);

[Ursula Trigos-Raczkowski]

but the input x has to do with the bounds of the error function which is an integral of t.

[Sindar]

You are mixing up "x, the input to the function" and "x, the value where you evaluate the function". There are a few ways you could fix your code, but

taylor(erf(x),t)

doesn't make sense. It's (almost exactly) like asking for d[f(x)]/dy instead of d[f(x)]/dx.

syms k x t 
x0=2;
for n=1:20
    N(n)=n;
    % Taylor series of erf(x) with respect to x, centered at 0, order n
    tayterm(n)=taylor(erf(x),x,0,'Order',n);
    % error between taylor apprx and value, at chosen x0
    ercol2(n) = double(erf(x0)-tayterm(n));
    % issue with asymterm was replacing the first of the x's with 2
    asymterm(n)=1-2/sqrt(pi)*exp(-x^2)*(symsum((-1)^k*x^(2*k+1)/((2*k+1)*factorial(k)),k,0,n-1));
    ercol4(n) = erf(x0)-asymterm(n);
end

[Ursula Trigos-Raczkowski]

Okay, this is giving me the following error:

Error using symengine

Unable to convert expression into double array.

Error in sym/double (line 700)

Xstr = mupadmex('symobj::double', S.s, 0);

Error in testing (line 19)

T = table(transpose(N),transpose(double(tayterm)),transpose(ercol2), transpose(asymterm),transpose(ercol4));

[Sindar]

You are trying to turn a symbolic expression into a number. That doesn't work. You can either leave the symbolic expression alone or evaluate it for a particular input (using subs), depending on what you want in the table

Answer 1

[Walter Roberson]

syms X

tayterm(n) = taylor(erf(X),X,x,'Order',n)

You always need to taylor() a function, not a constant.

[Ursula Trigos-Raczkowski]

thanks for your comment, again, this is the wrong function, i want a taylor function with respect to t not X and it should be around 0 not around x

so the taylor approximation of erf(2) with 2 terms is something like

a taylor approximation of erf(2) in general is something like

the asymptotic approximtion of erf(2) with 2 terms is something like

[Ursula Trigos-Raczkowski]

how can i set a string with the taylor values and then later evaluate it at x=2?

[Sindar]

subs(tayterm(n),2)

[Ursula Trigos-Raczkowski]

where? in the table? inside transpose? in the loop?

[Walter Roberson]

syms t
tayterm(n) = subs( taylor(erf(t),t,0,'Order',n), t, x );

That would taylor around 0 but evaluate at 2