# Python | sympy.harmonic() method

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

harmonic(n)

The nth 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 nth 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 nth 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


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