Sum with alternate signs
02-06-2015, 02:26 PM (This post was last modified: 02-06-2015 02:28 PM by salvomic.)
Post: #1
 salvomic Senior Member Posts: 1,367 Joined: Jan 2015
Sum with alternate signs
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

∫aL√0mic (IT9CLU), HP Prime 50g 41CX 71b 42s 12C 15C - DM42 WP34s :: Prime Soft. Lib
02-06-2015, 04:47 PM
Post: #2
 retoa Member Posts: 168 Joined: Jan 2015
RE: Sum with alternate signs
Same problem in xcas and Maxima. Wolframalpha gives the right answer.
02-06-2015, 04:49 PM
Post: #3
 salvomic Senior Member Posts: 1,367 Joined: Jan 2015
RE: Sum with alternate signs
(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...

∫aL√0mic (IT9CLU), HP Prime 50g 41CX 71b 42s 12C 15C - DM42 WP34s :: Prime Soft. Lib
02-06-2015, 05:08 PM (This post was last modified: 02-06-2015 05:17 PM by Gilles.)
Post: #4
 Gilles Member Posts: 164 Joined: Oct 2014
RE: Sum with alternate signs
(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 ...
02-06-2015, 05:10 PM (This post was last modified: 02-06-2015 05:17 PM by retoa.)
Post: #5
 retoa Member Posts: 168 Joined: Jan 2015
RE: Sum with alternate signs
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)
02-06-2015, 05:18 PM
Post: #6
 salvomic Senior Member Posts: 1,367 Joined: Jan 2015
RE: Sum with alternate signs
(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()

∫aL√0mic (IT9CLU), HP Prime 50g 41CX 71b 42s 12C 15C - DM42 WP34s :: Prime Soft. Lib
02-06-2015, 06:55 PM
Post: #7
 parisse Senior Member Posts: 1,117 Joined: Dec 2013
RE: Sum with alternate signs
Indeed, for the approx value of Psi(x,1), Xcas calls the GSL, that is not available on the Prime.
02-06-2015, 07:03 PM
Post: #8
 salvomic Senior Member Posts: 1,367 Joined: Jan 2015
RE: Sum with alternate signs
(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

∫aL√0mic (IT9CLU), HP Prime 50g 41CX 71b 42s 12C 15C - DM42 WP34s :: Prime Soft. Lib
02-07-2015, 06:46 AM
Post: #9
 parisse Senior Member Posts: 1,117 Joined: Dec 2013
RE: Sum with alternate signs
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
02-07-2015, 10:11 AM
Post: #10
 salvomic Senior Member Posts: 1,367 Joined: Jan 2015
RE: Sum with alternate signs
(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...

∫aL√0mic (IT9CLU), HP Prime 50g 41CX 71b 42s 12C 15C - DM42 WP34s :: Prime Soft. Lib
05-13-2015, 08:09 PM
Post: #11
 salvomic Senior Member Posts: 1,367 Joined: Jan 2015
RE: Sum with alternate signs
the problem is now solved with the firmware 7820!