MathGroup Archive 2009

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Infinite series

  • To: mathgroup at smc.vnet.net
  • Subject: [mg105701] Re: [mg105683] Infinite series
  • From: "Tony Harker" <a.harker at ucl.ac.uk>
  • Date: Wed, 16 Dec 2009 06:16:55 -0500 (EST)
  • References: <200912151227.HAA15202@smc.vnet.net>

FullSimplify will do it, or you can sneak round the problem with

Sum[Apart[1/((2*m - 3)^2*(2*m - 1)*(2*m + 1)^2)], {m, 2, Infinity, 
    2}] - Sum[
   Apart[1/((2*m - 3)^2*(2*m - 1)*(2*m + 1)^2)], {m, 1, Infinity, 
    2}] // Simplify

 Tony Harker

Dr A.H. Harker
Department of Physics and Astronomy
University College London
Gower Street
London
WC1E 6BT

Tel: (44)(0) 2076793404
E:    a.harker at ucl.ac.uk

 EDUCATION, n. That which discloses to the wise and disguises from the
foolish their lack of understanding. (Ambrose Bierce, The Devil's
Dictionary, 1911)
 

]-> -----Original Message-----
]-> From: Dr. C. S. Jog [mailto:jogc at mecheng.iisc.ernet.in] 
]-> Sent: 15 December 2009 12:27
]-> To: mathgroup at smc.vnet.net
]-> Subject: [mg105683] Infinite series
]-> 
]-> 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
]-> 
]-> 
]-> 
]-> --
]-> This message has been scanned for viruses and dangerous 
]-> content by MailScanner, and is believed to be clean.
]-> 
]-> 
]-> -- 
]-> This message has been scanned for viruses and
]-> dangerous content by MailScanner, and is
]-> believed to be clean.
]-> 
]-> 
]-> 



  • References:
  • Prev by Date: Re: ParallelTable slows down computation
  • Next by Date: Re: Re: Animation with Sound in Mathematica?
  • Previous by thread: Re: Infinite series
  • Next by thread: Re: Infinite series