#
# PYTHON • MyCompiler
# Polygamma
# https://[Log in to view URL]
# Função Polygamma
# 
# 2026 Maio Dom, 24 — Seg, 25
# by 
# j
# 

import matplotlib.pyplot as plt
import numpy as np
import math

def pyg(m,z):

    max = 3000
    
    psi = 0.00
    
    for k in range(0,max+1):
        
        if ( (z+k) != 0 ):
            
            psi += 1/((z + k)**(m+1))
                
    psi = ((-1)**(m+1))*math.factorial(m)*psi

    return psi
        
def graf():

    plt.style.use('dark_background')

    x = []
    y = []

    xmin = -2
    xmax = 4
    n = 500
    max = 3500
    pico = 100

    delta = (xmax - xmin)/n

    for m in range(0,5):
        
        z = xmin

        x.clear()
        y.clear()
        
        while ( z <= xmax ):

            psi = pyg(m,z)
            
            # if ( ( abs( z - 1) < 0.01 ) and ( m == 3 ) ):
                
                # print(z,psi)

            if (abs(psi) < pico):
                
                x.append(z)
                y.append(psi)
            
            z += delta

        lbl = '$ ψ^' + str(m) + '$'
        plt.plot(x,y,'.',label=lbl)
        
    tit = 'Polygamma Function'

    # plt.axis('equal') 
    plt.title(tit)
    plt.legend()
    # plt.xticks([])  
    # plt.yticks([])
    plt.xlim([-2, 4])
    plt.ylim([-pico, pico])
    plt.grid(False)
    plt.show()

graf()