Infinite series
- To: mathgroup at smc.vnet.net
- Subject: [mg105683] Infinite series
- From: "Dr. C. S. Jog" <jogc at mecheng.iisc.ernet.in>
- Date: Tue, 15 Dec 2009 07:27:17 -0500 (EST)
Hi:
We have the following identity:
\sum_{m=1}^{infinity} (-1)^m/((2m-3)^2*(2m-1)*(2m+1)^2)=-Pi/32.
When we type the command,
In[1]:=Sum[(-1)^m/((2*m-3)^2*(2*m-1)*(2*m+1)^2),{m,Infinity}]
we get
2 1 1
-16 Pi + 2 Pi - HurwitzZeta[2, -(-)] - Zeta[2, -]
4 4
Out[1]= --------------------------------------------------
512
The command Simplify[%] does not simplify it further.
I am sure the above expression must be equal to -Pi/32, but a user would
prefer this answer than the above one.
Thanks and regards
C. S. Jog
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