I have a function which is integral of(bounds are from minus infinity to x) e^((-0.5)*t^2)/sqrt(2*pi) dt.
Its Taylor Series is: 0.5+[1/sqrt(2*pi)*(x+(-0.5)*x^3/1!*1/3+(-0.5)^2*x^5/2!*1/5+...+(-0.5)^25*x^51/25!*1/51+...
I need to write a function that keeps counting the series until the sum doesn't change...
I have written this code:
function fx=f(x)
clear all
clc
format long
x=input('Enter a value to expand around:');
fx=(1/sqrt(2*pi))*exp(-0.5*x.^2)
k=0;
term=x;
sum=0;
while (fx~=sum)
fx=sum;
k=k+1
term=term*(-0.5)*x^2/k*(2*k-1)/(2*k+1)
sum=sum+term
end
Fix=0.5+(sum/sqrt(2*pi))
exact_solution=0.5+0.5*erf(x/sqrt(2))
end
But I cannot get accurate solution. What is the problem with my code???