Matlab coding error using nest loops to calculate pi.

Question:

The value of p can also be expressed using the expression below as the summation of an infinite series. Please write an m file based on this equation to calculate p so that the value of p is accurate to the 8^th digit after the decimal. Please plot the value of p as a function of k.

My code is as follows:

%Value of pi to 8th digit after decimal: 3.14159265

%Following are functions to calculate each element of the series

function a=a(k)

a=4./(8*k+1);

end;

function b=b(k)

b=2/(8*k+4);

end;

function c=c(k)

c=1/(8*k+5);

end;

function d=d(k)

d=1/(8*k+6);

end;

%Value of pi=3.14159265, so an upper and lower limit must be set to break

%loop once the accuracy to the 8th digit is met

lowpi=3.1415926499;

highpi=3.1415926501;

k=0; %starting k

calculated_pi=0; %starting calculation of pi

while true

calculated_pi += (a(k)-b(k)-c(k)-d(k))./(16.^k);

if calculated_pi >= lowpi && calculated_pi

break;

end;

k += 1; %set increment of k

end

k %prints value of k needed to reach 8th decimal accuracy

format long

calculated_pi %prints value of pi

However, I keep getting an error message saying, " A nested function cannot be defined inside a control statement (if, while, for, switch or try/catch). " from the four functions defined at the beginning of my code. I don't understand how they are nested inside the while statement.

oo -316k(8k4 1 8k2 4 8k 1-5 8k1-6) 16k (8k + 1 8k +4 8k + 5 8k + 6 k=0