Re: Summation Formulae Table

*To*: mathgroup at smc.vnet.net*Subject*: [mg28472] Re: Summation Formulae Table*From*: O <O_member at newsranger.com>*Date*: Fri, 20 Apr 2001 04:24:20 -0400 (EDT)*Organization*: http://www.newsranger.com*References*: <9bjg2v$gs8@smc.vnet.net> <9bm4pg$j2k@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Paul, thank you for your attempt to answer my question, I am sure I am not forming it right. Let me try once again, maybe this time I can do better. Where or how can I find the list of patterns and rewrite rules that built-in mathematical functions like Exp and Zeta and others will match against? In[1]:= Sum[1/k^p,{k,1,Infinity}] Out[1]= Zeta[p] In[17]:= Sum[x^k/k!,{k,0,Infinity}] Out[17]= Exp[x] How can I see the definitions of built-in mathematical functions or the rules they are associated with? UpValues[] and DownValues[] return empty lists. Thanks again, O In article <9bm4pg$j2k at smc.vnet.net>, Paul Lutus says... > >"O D" <O_member at newsranger.com> wrote in message >news:9bjg2v$gs8 at smc.vnet.net... >> Is there a way to access the tables that Sum[] uses to simplify summations >into >> known functions like for example >> >> Sum[Exp[-a* n^2], {n, -Infinity, Infinity}] >> >> is simplified into >> >> EllipticTheta[3, 0, E^(-a)] > >This simplification does not use a table, it uses a deterministic algorithm. > >> >> Is there a way to use the table in reverse, to approximate a known >function? > >You need to offer a specific example of a problem and a Mathematica solution >that you would like to see in a different form. Also, if you are interested >in approximating functions, you may want to approach the problem >differently, using regression methods such as are offered by "Fit" and >related resources. > >-- >Paul Lutus >www.arachnoid.com > > > >