HP Prime (emulator): Zeta function query  Printable Version + HP Forums (https://archived.hpcalc.org/museumforum) + Forum: HP Museum Forums (https://archived.hpcalc.org/museumforum/forum1.html) + Forum: Old HP Forum Archives (https://archived.hpcalc.org/museumforum/forum2.html) + Thread: HP Prime (emulator): Zeta function query (/thread251705.html) 
HP Prime (emulator): Zeta function query  Paul Townsend (UK)  09292013 The HP Prime emulator seems to have difficulty with Zeta() of an odd positive integer, retaining the function call unevaluated even after Eval(). In a plot view such values show as "Undefined". What's going on? Zeta() is welldefined at these values and my WP34s (the real thing) has no difficulty evaluating Zeta(3) for example to be 1.20205...
Zeta() of an even integer is correctly handled returning the appropriate expression involving pi, and Zeta() of nonintegral values is also correctly handled.
Re: HP Prime (emulator): Zeta function query  Helge Gabert  09292013 In CAS mode, hit approx key, after the Prime returns Zeta(3), then you also get the desired numerical result (1.202...).
I agree, in plot view you get "undefined".
Re: HP Prime (emulator): Zeta function query  Paul Townsend (UK)  09292013 I wonder if it is evaluating Zeta(n) recursively using Zeta(n2)? Starting with Zetas(3) would result in the algorithm boggling on Zeta(1) and bombing out with an error.
Asking for Zeta(1) correctly returns infinity.
Re: HP Prime (emulator): Zeta function query  Helge Gabert  09292013 Yes, I bet that's it! The algorithm should change depending on the user input   but since this "only" affects odd integers > 1 it was probably either overlooked or deemed to be too much trouble to implement.
Re: HP Prime (emulator): Zeta function query  Paul Dale  09292013 Sounds like this is related to zeta(2n) being expressible relatively simply in terms of PI and the Bernoulli numbers whereas zeta(2n+1) are not. Zeta(3) is ApĂ©ry's constant which has been proven to be transcendental, there are infinite series expressions for it but nothing really simple and certainly nothing simpler than just zeta(3).
Re: HP Prime (emulator): Zeta function query  Gerson W. Barbosa  09292013 That's what I thought, but that works for noninteger values and this is defined for integers only. http://people.math.sfu.ca/~cbm/aands/page_807.htm (Abramowitz and Stegun: Handbook of Mathematical Functions, page 807, formula 23.2.16) Gerson. P.S.: This HP 50g program has the same behaviour regarding integer arguments.
%%HP: T(3)A(D)F(.); Edited: 29 Sept 2013, 6:54 p.m.
Re: HP Prime (emulator): Zeta function query  mjcohen  09292013 I don't think it has been proven transcendental  only irrational.
Re: HP Prime (emulator): Zeta function query  Paul Dale  09292013 You are correct, the proof was for irrationality only.
 Pauli
