Python Code

Write a function that estimates the Omega constant, which is the value of the real root of f (x; 1), where f (x; a) = exx a, to sixteen decimal places using the xed-point iteration,

xn+1 = xn + ex x , 1+ex

using the initial guess x0 = 0. The root of f (x; a) is called the Lambert W function of a, which is dened as the root of the function implicit function

xex = a

so that LambertW (a) = x. This function is also called the omega function or the product logarithm, and appears frequently in the study of delay dierential equations, quantum mechanics, and enzyme kinetics.

(a) The function must be named compute_lambertW1_pi verbatim.

(b) The function will not take any parameters and will return a oating-point number as output where

the return value is LambertW (1).

(c) Do NOT use the denition of Lambert W function from any libraryyou must write your own!