I am a master's student, I have a little experience in harmonic numbers. I know the $H_{n} = \sum_{k=1}^{n} \frac{1}{k}$ .
I am wondering what the $H_{(\frac{1}{k}-1)}$ is. I am trying to rewrite it as a series like $H_{n}$. I got $H_{(\frac{1}{k}-1)} = \digamma(1/k)+ \psi$, But I think there is something wrong because when I try numbers in Python I get different results. How can I write it as a series and Digamma function?
Any help is welcome.