Sum with alternate signs - Printable Version +- HP Forums ( https://www.hpmuseum.org/forum)+-- Forum: HP Calculators (and very old HP Computers) ( /forum-3.html)+--- Forum: HP Prime ( /forum-5.html)+--- Thread: Sum with alternate signs ( /thread-3024.html) |

Sum with alternate signs - salvomic - 02-06-2015 02:26 PM
hi, there is a way in Prime to do this sum? \[ \sum_{k=1}^{\infty}{\frac {(-1)^{k+1}}{k^{2}} } \] the value is \( \frac {π^{2}}{12} \) HP Prime gives symbolic form, not the value of the sum... Thanks Salvo RE: Sum with alternate signs - retoa - 02-06-2015 04:47 PM
Same problem in xcas and Maxima. Wolframalpha gives the right answer. RE: Sum with alternate signs - salvomic - 02-06-2015 04:49 PM
(02-06-2015 04:47 PM)retoa Wrote: Same problem in xcas and Maxima. Wolframalpha gives the right answer. yes, in fact! As I like much more Prime (and HP 50g), I wonder why they don't... RE: Sum with alternate signs - Gilles - 02-06-2015 05:08 PM
(02-06-2015 02:26 PM)salvomic Wrote: hi, You can do \[ \sum_{k=1}^{\infty}{\frac {-1}{(2*k)^{2}} } + \sum_{k=1}^{\infty}{\frac {1}{(2*k-1)^{2}} } \] By the way I get the correct answer on the HP50G but my Prime seems unable to calculate Psi(1/2,1) in a numeric value. I get : 1/4*Psi(1/2,1)-Pi²/24 Same on 50G then ->NUM returns 0.8224... On the Prime ~ don't 'solve' Psi(0.5,1) . Strange ... RE: Sum with alternate signs - retoa - 02-06-2015 05:10 PM
I also tried to decompose it in \( \sum_{k=1}^{\infty}(\frac{1}{(2k-1)^2}-\frac{1}{(2k)^2}) \) to avoid the (-1)^(k+1), but I did not get the wanted result. Still the Psi(1/2,1) RE: Sum with alternate signs - salvomic - 02-06-2015 05:18 PM
(02-06-2015 05:08 PM)Gilles Wrote: You can do thanks a lot, Gilles, yes I see that Prime don't approx Psi1/2,1); my HP50 does it. Hope in a next firmware to have the symbolic result (π^2/12), more interesting than Psi() RE: Sum with alternate signs - parisse - 02-06-2015 06:55 PM
Indeed, for the approx value of Psi(x,1), Xcas calls the GSL, that is not available on the Prime. RE: Sum with alternate signs - salvomic - 02-06-2015 07:03 PM
(02-06-2015 06:55 PM)parisse Wrote: Indeed, for the approx value of Psi(x,1), Xcas calls the GSL, that is not available on the Prime. I understand. There is no other way to approximate Psi on Prime? thank you RE: Sum with alternate signs - parisse - 02-07-2015 06:46 AM
No built-in yet. Maybe I'll implement something, in the meantime you can write a user program http://people.math.sfu.ca/~cbm/aands/page_260.htm RE: Sum with alternate signs - salvomic - 02-07-2015 10:11 AM
(02-07-2015 06:46 AM)parisse Wrote: No built-in yet. Maybe I'll implement something, in the meantime you can write a user program ok, thank you for information! I'll think to write a program, maybe... RE: Sum with alternate signs - salvomic - 05-13-2015 08:09 PM
the problem is now solved with the firmware 7820! Answer: -π/12 |