that definition only converges for Re(z)>1. for Re(z)<=1, you need alternate formulas

Yes. Riemann gives them in the paper, including derivation, it’s just a bit annoying to type/read them here because hn doesn’t support mathjaxx.

	▲	zombot 2 hours ago \| parent [-]
		I'm just not mathematician enough to convert that into a C function. Let alone one that is both efficient and reasonably accurate.