eps

from math import log


def tailor(x):
    a_n=float(-1.0*pow(x,2))/4.0
    n=1
    sum=a_n
    eps = pow(10,-6)
    '''
    an+1=an*qn
    '''
    while True:
        q_n = (-1.0*x*x*n)/((n+1.0) * (2.0*n+1.0) * (2.0*n+2.0))
        a_n1=a_n*q_n
        r=abs(a_n1-a_n)
        sum+=a_n1
        a_n=a_n1
        n+=1
        if r<eps:
            break
    return sum


def fun(x):
    return 0.577215+log(x)+tailor(x)

def lagran(x, fi, xi):
    sum=0
    for i in range(len(xi)):
        p=1
        for j in range(len(xi)):
            if i != j:
                p*=(x-xi[j])/(xi[i]-xi[j])
        sum+=fi[i]*p
    return sum


import numpy as np


print("Tailor")
a=0.4
b=4.0



print("max esp")

for l in np.arange(25,300,10):
  n=l
  h=b/n
  i=a
  f=[]
  x=[]
  # print("x\tf(x)")
  while i<=b+h:
      x.append(i)
      f.append(fun(i))
      i+=h
  # for i,j in zip(f,x):
      # print(f"{j:.1f}\t{i}")

  # print("\nLagrang")
  # print("x\tL(x)\t\t\tf(x)\t\t\tesp")
  e_max=0
  j=a+0.1
  while j<=b:
      L=lagran(j,f,x)
      fu=fun(j)
      e=abs(fu-L)
      if e>e_max:
          e_max=e
      # print(f"{j:.1f}\t{L}\t{fu}\t{e}")
      j+=h
  print(f"{n}\t{e_max}")