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# Re: summations!

Rahul Swaminathan wrote:
>
> guys i am new to mathematica ... and want to do summations... if i have
> 2 nested summations one ranging from say i = 0 to i = N and the inner
> one from j = 0 to j = M , how do i represent it in mathematica for the
> under.
>
> \sigma{_i = 0}{N} \sigma{_j = 0}{M} [Sin ( \theta{_i,_j} ) * Cos (
> \phi{_i} ) ]
>
> an early responce would be great:)
>
> regards,
> -sr

Copy the notation that you have given In[1]:=
Sum[Sum[a[i,j],{j,0,M}],{i,0,N}]

Out[1]=
Sum[Sum[a[i, j], {j, 0, M}], {i, 0, N}]

or sum over two indices (notice that the index for the outer summation
in the previous form comes first)

In[2]:=
Sum[a[i,j],{i,0,N},{j,0,M}]

Out[2]=
Sum[a[i, j], {i, 0, N}, {j, 0, M}]

Numerical version of this:

In[3]:=
Sum[a[i,j],{i,0,2},{j,0,3}]

Out[3]=
a[0, 0] + a[0, 1] + a[0, 2] + a[0, 3] + a[1, 0] + a[1, 1] +

a[1, 2] + a[1, 3] + a[2, 0] + a[2, 1] + a[2, 2] + a[2, 3]

Limits for inner indices can be functions of outer indices In[4]:=
Sum[Sum[a[i,j],{j,0,i+1}],{i,0,2}]

Out[4]=
a[0, 0] + a[0, 1] + a[1, 0] + a[1, 1] + a[1, 2] + a[2, 0] +

a[2, 1] + a[2, 2] + a[2, 3]

In the summation over multiple indices version this become: Limits for
later indices can be functions of earlier indices.

In[5]:=
Sum[a[i,j],{i,0,2},{j,0,i+1}]

Out[5]=
a[0, 0] + a[0, 1] + a[1, 0] + a[1, 1] + a[1, 2] + a[2, 0] +

a[2, 1] + a[2, 2] + a[2, 3]

--
Allan Hayes
Training and Consulting
Leicester, UK
hay@haystack.demon.co.uk
http://www.haystack.demon.co.uk
voice: +44 (0)116 271 4198
fax: +44 (0)116 271 8642



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