Galerien besonderer Summen und Integrale erstellen 

Erstellen Sie eine Galerie multivariater Summen.

Die gesamte Wolfram-Language Eingabe zeigenEingabe verbergen

In[1]:=

X 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=

Erstellen Sie eine Galerie bestimmter Integrale.

Die gesamte Wolfram-Language Eingabe zeigenEingabe verbergen

In[2]:=

X defint = Inactivate[{\!\( \*SubsuperscriptBox[\(\[Integral]\), \(0\), \(\[Infinity]\)]\( \*FractionBox[\(1\), \( \*SuperscriptBox[\(x\), \(4\)] + \*SuperscriptBox[\(x\), \(2\)] + 2\)] \[DifferentialD]x\)\), \!\( \*SubsuperscriptBox[\(\[Integral]\), \(0\), FractionBox[\(\[Pi]\), \(2\)]]\(Cos[ \*SuperscriptBox[\(Sin[x]\), \(2\)]] \[DifferentialD]x\)\), \!\( \*SubsuperscriptBox[\(\[Integral]\), \(0\), \(\[Infinity]\)]\( \*SuperscriptBox[\(AiryAi[x]\), \(2\)] \[DifferentialD]x\)\), \!\( \*SubsuperscriptBox[\(\[Integral]\), \(0\), \(1\)]\(Ceiling[ \*SuperscriptBox[\(x\), \(2\)] + Abs[3\ x - 1]] \[DifferentialD]x\)\), \!\( \*SubsuperscriptBox[\(\[Integral]\), \(0\), \(2\)]\(Floor[ \*SuperscriptBox[\(x\), \(2\)]] \[DifferentialD]x\)\), \!\( \*SubsuperscriptBox[\(\[Integral]\), \(0\), \(1\)]\( \*FractionBox[\(Log[ \*FractionBox[\(1\), \(2\)]\ \((1 + \*SqrtBox[\(1 + 4\ x\)])\)]\), \(x\)] \[DifferentialD]x\)\), \!\( \*SubsuperscriptBox[\(\[Integral]\), \(0\), \(\[Infinity]\)]\( \*FractionBox[\( \*UnderoverscriptBox[\(\[Product]\), \(k = 0\), \(5\)]Sin[ \*FractionBox[\(x\), \(2\ k + 1\)]]\), SuperscriptBox[\(x\), \(6\)]] \[DifferentialD]x\)\)}, Product | Integrate]; 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[defint] // TraditionalForm

Out[2]//TraditionalForm=