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Zeta function

The Riemann zeta function ζ is defined by

and is used in number theory to study the distribution of prime numbers.

 


Explanation

For natural numbers you write the function as

and for complex numbers as

 


Examples

The French nathematician Jean Baptiste Fourier used the zeta function to calculate the number π as

The Swiss mathematician Leonhard Euler used the function also and calculated π as

 


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