Create Galleries of Special Sums and Integrals

Create a gallery of multivariate sums.

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In[1]:=

multisums = Inactivate[{\!\(
\*UnderoverscriptBox[\(\[Sum]\), \(m = 2\), \(\[Infinity]\)]\(
\*UnderoverscriptBox[\(\[Sum]\), \(n = 1\), \(\[Infinity]\)]
\*FractionBox[\(1\), 
SuperscriptBox[\((2\ n)\), \(m\)]]\)\), \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(m = 1\), \(\[Infinity]\)]\(
\*UnderoverscriptBox[\(\[Sum]\), \(n = 1\), \(\[Infinity]\)]
\*FractionBox[\(1\), 
SuperscriptBox[\((4\ n - 1)\), \(2\ m\)]]\)\), \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(\[Infinity]\)]\(
\*UnderoverscriptBox[\(\[Sum]\), \(j = 1\), \(\[Infinity]\)]
\*FractionBox[\(Zeta[i + j]\), 
SuperscriptBox[\(2\), \(i + j\)]]\)\),  \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(\[Infinity]\)]\(
\*UnderoverscriptBox[\(\[Sum]\), \(j = 1\), \(\[Infinity]\)]
\*FractionBox[\(1\), \(\((i + j)\)!\)]\)\), \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(\[Infinity]\)]\(
\*UnderoverscriptBox[\(\[Sum]\), \(j = 1\), \(\[Infinity]\)]
\*FractionBox[\(1\), \(Max[i, j]!\)]\)\), \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(\[Infinity]\)]\(
\*UnderoverscriptBox[\(\[Sum]\), \(j = 1\), \(\[Infinity]\)]
\*FractionBox[\(1\), 
SuperscriptBox[\(Max[i, j]\), \(3\)]]\)\), \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(\[Infinity]\)]\(
\*UnderoverscriptBox[\(\[Sum]\), \(j = 1\), \(\[Infinity]\)]\(
\*UnderoverscriptBox[\(\[Sum]\), \(k = 1\), \(\[Infinity]\)]
\*FractionBox[\(1\), 
SuperscriptBox[\((i\ j + j\ k)\), \(s\)]]\)\)\), \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(m = 1\), \(\[Infinity]\)]\(
\*UnderoverscriptBox[\(\[Sum]\), \(n = 1\), \(\[Infinity]\)]
\*FractionBox[\(Zeta[m + 2\ n]\), 
SuperscriptBox[\(4\), \(
\*FractionBox[\(m\), \(2\)] + n\)]]\)\), \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(i = 0\), \(\[Infinity]\)]\(
\*UnderoverscriptBox[\(\[Sum]\), \(j = 0\), \(\[Infinity]\)]\(
\*UnderoverscriptBox[\(\[Sum]\), \(k = 1\), \(\[Infinity]\)]
\*FractionBox[\(1\), 
SuperscriptBox[\((i + 2\ j + k)\), \(4\)]]\)\)\)}, Sum]; 
FormulaGallery[forms_List] := 
 Module[{vals = ParallelMap[Activate, forms]}, 
  Column[Table[
    Style[forms[[r]] == vals[[r]], ScriptLevel -> 0], {r, 
     Length[forms]}], Dividers -> All, Alignment -> "\[LongEqual]", 
   Background -> LightPurple, Spacings -> 1]]; 
FormulaGallery[multisums] // TraditionalForm

Out[1]//TraditionalForm=

Create a gallery of definite integrals.

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Out[2]//TraditionalForm=

Wolfram Mathematica

Create Galleries of Special Sums and Integrals

Mathematica

Wolfram Mathematica

Create Galleries of Special Sums and Integrals

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Mathematica