Limit of the Logarithmic Derivative

Click on the image for a detailed proof

\lim_{s\rightarrow 1}\left(\frac{\zeta'(s)}{\zeta(s)}+\frac{1}{s-1}\right)=\gamma

The logarithmic derivative of a function can derive crucial properties. By applying this approach to the Riemann Zeta Function, we encounter the well-known Euler-Mascheroni constant.

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First Functional Equation
First Functional Equation
Infinite zeros on the Critical Line
Infinite zeros on the Critical Line
Representation by Euler-Maclaurin Formula
Representation by Euler-Maclaurin Formula
Relation to the Sine Function
Relation to the Sine Function
On the number of primes less than a given quantity
On the number of primes less than a given quantity
Relation to the Gamma Function 1
Relation to the Gamma Function 1

See all Formulas for the Riemann Zeta…

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