1. Sigma

Sigma ($ \ Sigma $): Sum of multiple numbers

\sum_{k=1}^n a_k = a_1 + a_2 + \cdots + a_n

\sum_{k} a_k = a_1 + a_2 + \cdots + a_n

import numpy as np

a = np.array([1, 2, 3, 4, 5])
print(np.sum(a))

`Execution result`

2. Number of napiers

Napier number $ e $

e = 2.71828 18284 59045 23536 02874 71352 …

y=e^x=\exp(x)

This formula has a very convenient feature that the formula does not change even if it is differentiated.

import numpy as np

def get_exp(x):
    return np.exp(x)
    
print(get_exp(1))

`Execution result`


2.718281828459045

graph display

↓ Please refer to the article I wrote earlier for graph display. #Python basics (#matplotlib)

import numpy as np
import matplotlib.pyplot as plt

def get_exp(x):
    return np.exp(x)

x = np.linspace(-3, 3, num=100)
y = get_exp(x)

#Axis label
plt.xlabel("x val")
plt.ylabel("y val")

#axis
plt.axhline(0, color = "gray")
plt.axvline(0, color = "gray")

#plt.hlines(y=[0], colors='b', linestyles='dashed', linewidths=1)
#Graph title
plt.title("Graph Name")

#Specify plot legend and line style
plt.plot(x, y, label="y")
plt.legend() #Show legend

plt.show()

3. Natural logarithm

x = e^y

When $ y = \log_{e} x $


import numpy as np

def get_log(x):
    return np.log(x)
    
print(get_log(1))
# 0.0

graph display

import numpy as np
import matplotlib.pyplot as plt

def get_log(x):
    return np.log(x)

x = np.linspace(0.001, 3, num=1000)
y = get_log(x)

#Axis label
plt.xlabel("x val")
plt.ylabel("y val")

#axis
plt.axhline(0, color = "gray")
plt.axvline(0, color = "gray")

#Graph title
plt.title("Graph Name")

#Specify plot legend and line style
plt.plot(x, y, label="y")
plt.legend() #Show legend

plt.show()