Post Reply 
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
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 39s 35s 12C 15C - DM42, DM41X - WP34s Prime Soft. Lib
Visit this user's website Find all posts by this user
Quote this message in a reply
02-06-2015, 04:47 PM
Post: #2
RE: Sum with alternate signs
Same problem in xcas and Maxima. Wolframalpha gives the right answer.
Find all posts by this user
Quote this message in a reply
02-06-2015, 04:49 PM
Post: #3
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 39s 35s 12C 15C - DM42, DM41X - WP34s Prime Soft. Lib
Visit this user's website Find all posts by this user
Quote this message in a reply
02-06-2015, 05:08 PM (This post was last modified: 02-06-2015 05:17 PM by Gilles.)
Post: #4
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 ...
Find all posts by this user
Quote this message in a reply
02-06-2015, 05:10 PM (This post was last modified: 02-06-2015 05:17 PM by retoa.)
Post: #5
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)
Find all posts by this user
Quote this message in a reply
02-06-2015, 05:18 PM
Post: #6
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() Smile

∫aL√0mic (IT9CLU) :: HP Prime 50g 41CX 71b 42s 39s 35s 12C 15C - DM42, DM41X - WP34s Prime Soft. Lib
Visit this user's website Find all posts by this user
Quote this message in a reply
02-06-2015, 06:55 PM
Post: #7
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.
Find all posts by this user
Quote this message in a reply
02-06-2015, 07:03 PM
Post: #8
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 39s 35s 12C 15C - DM42, DM41X - WP34s Prime Soft. Lib
Visit this user's website Find all posts by this user
Quote this message in a reply
02-07-2015, 06:46 AM
Post: #9
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
Find all posts by this user
Quote this message in a reply
02-07-2015, 10:11 AM
Post: #10
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... Smile

∫aL√0mic (IT9CLU) :: HP Prime 50g 41CX 71b 42s 39s 35s 12C 15C - DM42, DM41X - WP34s Prime Soft. Lib
Visit this user's website Find all posts by this user
Quote this message in a reply
05-13-2015, 08:09 PM
Post: #11
RE: Sum with alternate signs
the problem is now solved with the firmware 7820!

Answer: -π/12

∫aL√0mic (IT9CLU) :: HP Prime 50g 41CX 71b 42s 39s 35s 12C 15C - DM42, DM41X - WP34s Prime Soft. Lib
Visit this user's website Find all posts by this user
Quote this message in a reply
Post Reply 




User(s) browsing this thread: 2 Guest(s)