*To*: mathgroup@smc.vnet.net*Subject*: [mg10973] Re: summations!*From*: Allan Hayes <hay@haystack.demon.co.uk>*Date*: Sun, 15 Feb 1998 02:10:38 -0500*References*: <6c3dq1$1ct@smc.vnet.net>

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