Euler created the following expression for the Euler-Mascheroni constant: $$\gamma=\sum^\infty_{k=1} \left(\frac{1}{k}-\ln\left(1+\frac{1}{k} \right)\right)$$ This converges more rapidly than the original definition: $$\gamma=\lim_{x\rightarrow \infty} H(x)-\ln(x)$$ Where $H(x)$ is the $x$th harmonic number. Anyway, I derived a generalization of Euler's sum: $$\gamma=\sum^\infty_{k=1} \left(\frac{1}{k}-\frac{\ln\left(1+\frac{z}{k} \right)}{z}\right)-\frac{\ln (z!)}{z}$$ Where $z$ is literally any number. I derived this formula using the Weierstrass definition of the Gamma function and then simplifying. Is this novel?
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