Re: Re: Harmonic Numbers
- To: mathgroup at smc.vnet.net
- Subject: [mg107950] Re: [mg107919] Re: [mg107881] Harmonic Numbers
- From: leigh pascoe <leigh at evry.inserm.fr>
- Date: Wed, 3 Mar 2010 05:54:25 -0500 (EST)
- References: <201003020834.DAA03875@smc.vnet.net> <201003021256.HAA14588@smc.vnet.net>
Le 02/03/2010 13:56, leigh pascoe a =C3=A9crit :
> Le 02/03/2010 09:34, Chris H. Fleming a =C3=A9crit :
>
>> Sum[k/((k^2 + 1) (k^2 + 4)), {k, 1, \[Infinity]}]
>>
>> Sum does not converge.
>>
>> NSum[k/((k^2 + 1) (k^2 + 4)), {k, 1, \[Infinity]}]
>>
>> 0.206647
>>
>>
>> Fortunately I know how to do this sum by hand, but Mathematica can
>> usually handle these Harmonic number functions pretty well.
>>
>> Does anyone know a way of massaging this into a form Mathematica can
>> digest?
>>
>>
>>
>>
> Mathematica 7.0.1.0
> In[3]:= NSum[k/((k^2+1) (k^4+4)),{k,1,\[Infinity]}]
> Out[3]= 0.125
> In[4]:= Sum[k/((k^2+1) (k^4+4)),{k,1,\[Infinity]}]
> Out[4]= 1/8
>
> Leigh
>
>
>
Correction of previous reply
In[16]:= $Version
Out[16]= 7.0 for Microsoft Windows (32-bit) (February 18, 2009)
In[17]:= NSum[k/((k^2+1) (k^2+4)),{k,1,\[Infinity]}]
Out[17]= 0.206647
In[18]:= Sum[k/((k^2 + 1) (k^2 + 4)), {k, 1, \[Infinity]}]
Out[18]= -(1/2) RootSum[10 + 14 #1 + 11 #1^2 + 4 #1^3 + #1^4 &,
PolyGamma[0, -#1]/(7 + 4 #1 + 2 #1^2) &]
In[19]:= N[%]
Out[19]= 0.206647 + 0. I
- References:
- Harmonic Numbers
- From: "Chris H. Fleming" <chris_h_fleming@yahoo.com>
- Re: Harmonic Numbers
- From: leigh pascoe <leigh@evry.inserm.fr>
- Harmonic Numbers