Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site ContributeEmail CommentsSign the Guestbook

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

Download All Introductions For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











Csch






Mathematica Notation

Traditional Notation









Elementary Functions > Csch[z] > Integration > Indefinite integration > Involving functions of the direct function and hyperbolic functions > Involving algebraic functions of the direct function and hyperbolic functions > Involving sinh and cosh





http://functions.wolfram.com/01.23.21.0459.01









  


  










Input Form





Integrate[((-2 Cosh[z]^3 (-1 + Sinh[z]) + Cosh[2 z] Sinh[z]) Csch[z]^2)/ Sqrt[-5 + Sinh[z]^2], z] == -(ArcTan[(Sqrt[10] Cosh[z])/Sqrt[-11 + Cosh[2 z]]]/Sqrt[5]) - (2 ArcTan[Sqrt[-11 + Cosh[2 z]]/Sqrt[10]])/Sqrt[5] + 2 ArcTanh[(Sqrt[2] Sinh[z])/Sqrt[-11 + Cosh[2 z]]] + (1/5) Sqrt[2] Sqrt[-11 + Cosh[2 z]] Csch[z] + 2 Log[Sqrt[2] Cosh[z] + Sqrt[-11 + Cosh[2 z]]] - (2 Sqrt[2] Sqrt[-11 + Cosh[2 z]] Sqrt[(-11 + Cosh[2 z])/(1 + Cosh[z])^2])/ Sqrt[(-11 + Cosh[2 z]) Sech[z/2]^4]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", SuperscriptBox[RowBox[List["Cosh", "[", "z", "]"]], "3"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Sinh", "[", "z", "]"]]]], ")"]]]], "+", RowBox[List[RowBox[List["Cosh", "[", RowBox[List["2", " ", "z"]], "]"]], " ", RowBox[List["Sinh", "[", "z", "]"]]]]]], ")"]], SuperscriptBox[RowBox[List["Csch", "[", "z", "]"]], "2"], " "]], SqrtBox[RowBox[List[RowBox[List["-", "5"]], "+", SuperscriptBox[RowBox[List["Sinh", "[", "z", "]"]], "2"]]]]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["ArcTan", "[", FractionBox[RowBox[List[SqrtBox["10"], " ", RowBox[List["Cosh", "[", "z", "]"]]]], SqrtBox[RowBox[List[RowBox[List["-", "11"]], "+", RowBox[List["Cosh", "[", RowBox[List["2", " ", "z"]], "]"]]]]]], "]"]], SqrtBox["5"]]]], "-", FractionBox[RowBox[List["2", " ", RowBox[List["ArcTan", "[", FractionBox[SqrtBox[RowBox[List[RowBox[List["-", "11"]], "+", RowBox[List["Cosh", "[", RowBox[List["2", " ", "z"]], "]"]]]]], SqrtBox["10"]], "]"]]]], SqrtBox["5"]], "+", RowBox[List["2", " ", RowBox[List["ArcTanh", "[", FractionBox[RowBox[List[SqrtBox["2"], " ", RowBox[List["Sinh", "[", "z", "]"]]]], SqrtBox[RowBox[List[RowBox[List["-", "11"]], "+", RowBox[List["Cosh", "[", RowBox[List["2", " ", "z"]], "]"]]]]]], "]"]]]], "+", RowBox[List[FractionBox["1", "5"], " ", SqrtBox["2"], " ", SqrtBox[RowBox[List[RowBox[List["-", "11"]], "+", RowBox[List["Cosh", "[", RowBox[List["2", " ", "z"]], "]"]]]]], " ", RowBox[List["Csch", "[", "z", "]"]]]], "+", RowBox[List["2", " ", RowBox[List["Log", "[", RowBox[List[RowBox[List[SqrtBox["2"], " ", RowBox[List["Cosh", "[", "z", "]"]]]], "+", SqrtBox[RowBox[List[RowBox[List["-", "11"]], "+", RowBox[List["Cosh", "[", RowBox[List["2", " ", "z"]], "]"]]]]]]], "]"]]]], "-", FractionBox[RowBox[List["2", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List[RowBox[List["-", "11"]], "+", RowBox[List["Cosh", "[", RowBox[List["2", " ", "z"]], "]"]]]]], " ", SqrtBox[FractionBox[RowBox[List[RowBox[List["-", "11"]], "+", RowBox[List["Cosh", "[", RowBox[List["2", " ", "z"]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", RowBox[List["Cosh", "[", "z", "]"]]]], ")"]], "2"]]]]], SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "11"]], "+", RowBox[List["Cosh", "[", RowBox[List["2", " ", "z"]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["Sech", "[", FractionBox["z", "2"], "]"]], "4"]]]]]]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> &#8747; </mo> <mrow> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> cosh </mi> <mn> 3 </mn> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> csch </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mtext> </mtext> </mrow> <msqrt> <mrow> <mrow> <msup> <mi> sinh </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 5 </mn> </mrow> </msqrt> </mfrac> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mrow> <msqrt> <mn> 10 </mn> </msqrt> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <msqrt> <mrow> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 11 </mn> </mrow> </msqrt> </mfrac> <mo> ) </mo> </mrow> <msqrt> <mn> 5 </mn> </msqrt> </mfrac> </mrow> <mo> - </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <msqrt> <mrow> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 11 </mn> </mrow> </msqrt> <msqrt> <mn> 10 </mn> </msqrt> </mfrac> <mo> ) </mo> </mrow> </mrow> <msqrt> <mn> 5 </mn> </msqrt> </mfrac> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> tanh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <msqrt> <mrow> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 11 </mn> </mrow> </msqrt> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 5 </mn> </mfrac> <mo> &#8290; </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 11 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <mrow> <mi> csch </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <msqrt> <mrow> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 11 </mn> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 11 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mfrac> <mrow> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 11 </mn> </mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mfrac> </msqrt> </mrow> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 11 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> sech </mi> <mn> 4 </mn> </msup> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </msqrt> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <apply> <sinh /> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <cosh /> <ci> z </ci> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <apply> <sinh /> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <csch /> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <sinh /> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -5 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <arctan /> <apply> <times /> <apply> <power /> <cn type='integer'> 10 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <cosh /> <ci> z </ci> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -11 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <arctan /> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -11 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <power /> <cn type='integer'> 10 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <arctanh /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <sinh /> <ci> z </ci> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -11 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 5 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -11 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <csch /> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <cosh /> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -11 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -11 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -11 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <cosh /> <ci> z </ci> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -11 </cn> </apply> <apply> <power /> <apply> <sech /> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", SuperscriptBox[RowBox[List["Cosh", "[", "z_", "]"]], "3"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Sinh", "[", "z_", "]"]]]], ")"]]]], "+", RowBox[List[RowBox[List["Cosh", "[", RowBox[List["2", " ", "z_"]], "]"]], " ", RowBox[List["Sinh", "[", "z_", "]"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Csch", "[", "z_", "]"]], "2"]]], SqrtBox[RowBox[List[RowBox[List["-", "5"]], "+", SuperscriptBox[RowBox[List["Sinh", "[", "z_", "]"]], "2"]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["ArcTan", "[", FractionBox[RowBox[List[SqrtBox["10"], " ", RowBox[List["Cosh", "[", "z", "]"]]]], SqrtBox[RowBox[List[RowBox[List["-", "11"]], "+", RowBox[List["Cosh", "[", RowBox[List["2", " ", "z"]], "]"]]]]]], "]"]], SqrtBox["5"]]]], "-", FractionBox[RowBox[List["2", " ", RowBox[List["ArcTan", "[", FractionBox[SqrtBox[RowBox[List[RowBox[List["-", "11"]], "+", RowBox[List["Cosh", "[", RowBox[List["2", " ", "z"]], "]"]]]]], SqrtBox["10"]], "]"]]]], SqrtBox["5"]], "+", RowBox[List["2", " ", RowBox[List["ArcTanh", "[", FractionBox[RowBox[List[SqrtBox["2"], " ", RowBox[List["Sinh", "[", "z", "]"]]]], SqrtBox[RowBox[List[RowBox[List["-", "11"]], "+", RowBox[List["Cosh", "[", RowBox[List["2", " ", "z"]], "]"]]]]]], "]"]]]], "+", RowBox[List[FractionBox["1", "5"], " ", SqrtBox["2"], " ", SqrtBox[RowBox[List[RowBox[List["-", "11"]], "+", RowBox[List["Cosh", "[", RowBox[List["2", " ", "z"]], "]"]]]]], " ", RowBox[List["Csch", "[", "z", "]"]]]], "+", RowBox[List["2", " ", RowBox[List["Log", "[", RowBox[List[RowBox[List[SqrtBox["2"], " ", RowBox[List["Cosh", "[", "z", "]"]]]], "+", SqrtBox[RowBox[List[RowBox[List["-", "11"]], "+", RowBox[List["Cosh", "[", RowBox[List["2", " ", "z"]], "]"]]]]]]], "]"]]]], "-", FractionBox[RowBox[List["2", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List[RowBox[List["-", "11"]], "+", RowBox[List["Cosh", "[", RowBox[List["2", " ", "z"]], "]"]]]]], " ", SqrtBox[FractionBox[RowBox[List[RowBox[List["-", "11"]], "+", RowBox[List["Cosh", "[", RowBox[List["2", " ", "z"]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", RowBox[List["Cosh", "[", "z", "]"]]]], ")"]], "2"]]]]], SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "11"]], "+", RowBox[List["Cosh", "[", RowBox[List["2", " ", "z"]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["Sech", "[", FractionBox["z", "2"], "]"]], "4"]]]]]]]]]]]










Date Added to functions.wolfram.com (modification date)





2002-12-18





© 1998-2014 Wolfram Research, Inc.