Python| sympy.harmonic() 方法

借助sympy.harmonic()方法，我们可以在 SymPy 中找到谐波数。

谐波(n)

第n^次谐波数由下式给出 - $\operatorname{H}_{n} = 1 + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{n}$ .

Syntax: harmonic(n)

Parameter:
n – It denotes the number upto which harmonic number is to be calculated.

Returns: Returns the n^th harmonic number.

示例 #1：

# import sympy 
from sympy import * 
  
n = 7
print("Value of n = {}".format(n))
   
# Use sympy.harmonic() method 
nth_harmonic = harmonic(n)  
      
print("Value of nth harmonic number : {}".format(nth_harmonic))  

输出：

Value of n = 7
Value of nth harmonic number : 363/140

谐波(n, m)

m阶的第n^个广义谐波数由下式给出 - $\operatorname{H}_{n, m} = \sum_{k=1}^{n} \frac{1}{k^m}$ .

Syntax: harmonic(n, m)

Parameter:
n – It denotes the number upto which harmonic number is to be calculated.
m – It denotes the order of the harmonic number.
Returns: Returns the nth harmonic number of order m.

示例 #2：

# import sympy 
from sympy import * 
  
n = 5
m = 2
print("Value of n = {} and m = {}".format(n, m))
   
# Use sympy.harmonic() method 
nth_harmonic_poly = harmonic(n, m)  
      
print("The nth harmonic number of order m : {}".format(nth_harmonic_poly))  

输出：

Value of n = 5 and m = 2
The nth harmonic number of order m : 5269/3600