Sum with alternate signs

02062015, 02:26 PM
(This post was last modified: 02062015 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 

02062015, 04:47 PM
Post: #2




RE: Sum with alternate signs
Same problem in xcas and Maxima. Wolframalpha gives the right answer.


02062015, 04:49 PM
Post: #3




RE: Sum with alternate signs
(02062015 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 

02062015, 05:08 PM
(This post was last modified: 02062015 05:17 PM by Gilles.)
Post: #4




RE: Sum with alternate signs
(02062015 02:26 PM)salvomic Wrote: hi, You can do \[ \sum_{k=1}^{\infty}{\frac {1}{(2*k)^{2}} } + \sum_{k=1}^{\infty}{\frac {1}{(2*k1)^{2}} } \] 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 ... 

02062015, 05:10 PM
(This post was last modified: 02062015 05:17 PM by retoa.)
Post: #5




RE: Sum with alternate signs
I also tried to decompose it in
\( \sum_{k=1}^{\infty}(\frac{1}{(2k1)^2}\frac{1}{(2k)^2}) \) to avoid the (1)^(k+1), but I did not get the wanted result. Still the Psi(1/2,1) 

02062015, 05:18 PM
Post: #6




RE: Sum with alternate signs
(02062015 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() ∫aL√0mic (IT9CLU) :: HP Prime 50g 41CX 71b 42s 39s 35s 12C 15C  DM42, DM41X  WP34s Prime Soft. Lib 

02062015, 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.


02062015, 07:03 PM
Post: #8




RE: Sum with alternate signs
(02062015 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 

02072015, 06:46 AM
Post: #9




RE: Sum with alternate signs
No builtin 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 

02072015, 10:11 AM
Post: #10




RE: Sum with alternate signs
(02072015 06:46 AM)parisse Wrote: No builtin 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... ∫aL√0mic (IT9CLU) :: HP Prime 50g 41CX 71b 42s 39s 35s 12C 15C  DM42, DM41X  WP34s Prime Soft. Lib 

05132015, 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 

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