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+--- 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,
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
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
\[ \sum_{k=1}^{\infty}{\frac {-1}{(2*k)^{2}} } + \sum_{k=1}^{\infty}{\frac {1}{(2*k-1)^{2}} } \]
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.
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
http://people.math.sfu.ca/~cbm/aands/page_260.htm
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