Bill Allombert on Sat, 16 Feb 2019 21:42:56 +0100 |
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Re: Evaluating Multiple Sums in PARI/GP |
On Sat, Feb 16, 2019 at 06:04:57PM +0100, Bill Allombert wrote: > On Fri, Feb 15, 2019 at 08:28:37PM +0300, kevin lucas wrote: > > I recently ran into problems attempting to formulate a PARI program that > > evaluated the expression > > > > sum(((-1)^(a+b+c))/(a^2 + b^2 + c^2)^s) > > > > for various complex values of s, with a,b,c running over Z^3/{(0,0,0)}. How > > should I attempt this? More generally, how should one set up iterated > > alternating sums like these? If, for instance I also wanted the > > eight-dimensional version of the above sum, how would I compute it? > > Is it not some kind of theta function ? Sorry I meant: the Mellin transform of a theta function, i.e. something that can be computed with lfunqf. for example for 2 variables: ? sumnum(a=1,sumnum(b=1,(a^2+b^2)^-4,S))*4 + sumnum(a=1,(a^2)^-4,S)*4 %25 = 4.2814306608057805856207768654374415990 ? L=lfunqf(matid(2)); ? lfun(L,4) %27 = 4.2814306608057805856207768654374415990 Cheers, Bill.