Python | sympy.harmonic() method

With the help of sympy.harmonic() method, we can find Harmonic numbers in SymPy.

harmonic(n)

The n^th harmonic number is given by – .

Syntax: harmonic(n) Parameter: n – It denotes the number upto which harmonic number is to be calculated. Returns: Returns the n^th harmonic number.

Example #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))

Output:

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

harmonic(n, m)

The n^th generalized harmonic number of order m is given by – .

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.

Example #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))

Output:

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