Evaluation of ζ(2) by the definition (sort of) [HP-42S & HP-71B]

[Gerson W. Barbosa]

(10-26-2021 02:13 PM)Ren Wrote:  What does ζ mean?

Basically it is a Greek letter, zeta, used do denote the mathematical function zeta(x), defined as

ζ(x) = 1 + 1/2ˣ + 1/3ˣ + 1/4ˣ + 1/5ˣ + …

where x is a real number greater than zero

When x = 1, for instance,it is equivalent to the harmonic function, ζ(x) = H(x) = 1 + 1/2 + 1/3+ 1/4 + 1/5 + …

Later the domain was extended to all the real axis and eventually to all the complex plane, when things started to become really interesting.

https://www.britannica.com/science/Riema...a-function