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
 











Coth






Mathematica Notation

Traditional Notation









Elementary Functions > Coth[z] > Integration > Indefinite integration > Involving functions of the direct function and hyperbolic functions > Involving algebraic functions of the direct function and hyperbolic functions > Involving cosh > Involving cosh(c z)(a+b coth(c z))beta





http://functions.wolfram.com/01.22.21.0401.01









  


  










Input Form





Integrate[Cosh[c z] (a + b Coth[c z])^\[Beta], z] == -(((b + (a + b)/(-1 + Coth[c z]))^\[Beta] ((-1 + \[Beta]) AppellF1[2 - \[Beta], 3/2, -\[Beta], 3 - \[Beta], -(2/(-1 + Coth[c z])), (a + b)/(b - b Coth[c z])] + (-2 + \[Beta]) AppellF1[1 - \[Beta], 3/2, -\[Beta], 2 - \[Beta], -(2/(-1 + Coth[c z])), (a + b)/(b - b Coth[c z])] (-1 + Coth[c z])) (a + b Coth[c z])^(-1 + \[Beta]) ((a + b Coth[c z])/(-1 + Coth[c z]))^ (1 - \[Beta]) Sinh[c z] Sqrt[Cosh[2 c z] + Sinh[2 c z]])/ (1 + (a + b)/(-b + b Coth[c z]))^\[Beta])/ (c (-2 + \[Beta]) (-1 + \[Beta]))










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], ")"]], "\[Beta]"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", FractionBox[RowBox[List["a", "+", "b"]], RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]]]]]]], ")"]], "\[Beta]"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[Beta]"]], ")"]], " ", RowBox[List["AppellF1", "[", RowBox[List[RowBox[List["2", "-", "\[Beta]"]], ",", FractionBox["3", "2"], ",", RowBox[List["-", "\[Beta]"]], ",", RowBox[List["3", "-", "\[Beta]"]], ",", RowBox[List["-", FractionBox["2", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]]]]]]], ",", FractionBox[RowBox[List["a", "+", "b"]], RowBox[List["b", "-", RowBox[List["b", " ", RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]]]]]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "\[Beta]"]], ")"]], " ", RowBox[List["AppellF1", "[", RowBox[List[RowBox[List["1", "-", "\[Beta]"]], ",", FractionBox["3", "2"], ",", RowBox[List["-", "\[Beta]"]], ",", RowBox[List["2", "-", "\[Beta]"]], ",", RowBox[List["-", FractionBox["2", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]]]]]]], ",", FractionBox[RowBox[List["a", "+", "b"]], RowBox[List["b", "-", RowBox[List["b", " ", RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]]]]]]]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]]]], ")"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], ")"]], RowBox[List[RowBox[List["-", "1"]], "+", "\[Beta]"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]]]]], ")"]], RowBox[List["1", "-", "\[Beta]"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["a", "+", "b"]], RowBox[List[RowBox[List["-", "b"]], "+", RowBox[List["b", " ", RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]]]]]]]]], ")"]], RowBox[List["-", "\[Beta]"]]], " ", RowBox[List["Sinh", "[", RowBox[List["c", " ", "z"]], "]"]], " ", SqrtBox[RowBox[List[RowBox[List["Cosh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]], "+", RowBox[List["Sinh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]]], ")"]]]], "/", RowBox[List["(", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "\[Beta]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[Beta]"]], ")"]]]], ")"]]]]]]]]










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> <mrow> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mi> coth </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mi> &#946; </mi> </msup> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#946; </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#946; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mfrac> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> <mrow> <mrow> <mi> coth </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mi> &#946; </mi> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> &#946; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <semantics> <msub> <mi> F </mi> <mn> 1 </mn> </msub> <annotation-xml encoding='MathML-Content'> <ci> AppellF1 </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mrow> <mrow> <mn> 2 </mn> <mo> - </mo> <mi> &#946; </mi> </mrow> <mo> ; </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <mi> &#946; </mi> </mrow> <mo> ; </mo> <mrow> <mn> 3 </mn> <mo> - </mo> <mi> &#946; </mi> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 2 </mn> <mrow> <mrow> <mi> coth </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> </mrow> </mrow> <mo> , </mo> <mfrac> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> <mrow> <mi> b </mi> <mo> - </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mi> coth </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> &#946; </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <semantics> <msub> <mi> F </mi> <mn> 1 </mn> </msub> <annotation-xml encoding='MathML-Content'> <ci> AppellF1 </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#946; </mi> </mrow> <mo> ; </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <mi> &#946; </mi> </mrow> <mo> ; </mo> <mrow> <mn> 2 </mn> <mo> - </mo> <mi> &#946; </mi> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 2 </mn> <mrow> <mrow> <mi> coth </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> </mrow> </mrow> <mo> , </mo> <mfrac> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> <mrow> <mi> b </mi> <mo> - </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mi> coth </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> coth </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mi> coth </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> &#946; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mrow> <mi> a </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mi> coth </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mrow> <mrow> <mi> coth </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#946; </mi> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mi> coth </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mi> b </mi> </mrow> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> &#946; </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <cosh /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <apply> <coth /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <ci> &#946; </ci> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <ci> c </ci> <apply> <plus /> <ci> &#946; </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <ci> &#946; </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <apply> <power /> <apply> <plus /> <apply> <coth /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> &#946; </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> &#946; </ci> <cn type='integer'> -1 </cn> </apply> <apply> <ci> AppellF1 </ci> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> </apply> <cn type='rational'> 3 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <apply> <coth /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <coth /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> &#946; </ci> <cn type='integer'> -2 </cn> </apply> <apply> <ci> AppellF1 </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> </apply> <cn type='rational'> 3 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <apply> <coth /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <coth /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <coth /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <apply> <coth /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <ci> &#946; </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <apply> <coth /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <coth /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <coth /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> </apply> <apply> <sinh /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <sinh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[RowBox[List["Cosh", "[", RowBox[List["c_", " ", "z_"]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a_", "+", RowBox[List["b_", " ", RowBox[List["Coth", "[", RowBox[List["c_", " ", "z_"]], "]"]]]]]], ")"]], "\[Beta]_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", FractionBox[RowBox[List["a", "+", "b"]], RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]]]]]]], ")"]], "\[Beta]"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[Beta]"]], ")"]], " ", RowBox[List["AppellF1", "[", RowBox[List[RowBox[List["2", "-", "\[Beta]"]], ",", FractionBox["3", "2"], ",", RowBox[List["-", "\[Beta]"]], ",", RowBox[List["3", "-", "\[Beta]"]], ",", RowBox[List["-", FractionBox["2", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]]]]]]], ",", FractionBox[RowBox[List["a", "+", "b"]], RowBox[List["b", "-", RowBox[List["b", " ", RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]]]]]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "\[Beta]"]], ")"]], " ", RowBox[List["AppellF1", "[", RowBox[List[RowBox[List["1", "-", "\[Beta]"]], ",", FractionBox["3", "2"], ",", RowBox[List["-", "\[Beta]"]], ",", RowBox[List["2", "-", "\[Beta]"]], ",", RowBox[List["-", FractionBox["2", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]]]]]]], ",", FractionBox[RowBox[List["a", "+", "b"]], RowBox[List["b", "-", RowBox[List["b", " ", RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]]]]]]]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]]]], ")"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], ")"]], RowBox[List[RowBox[List["-", "1"]], "+", "\[Beta]"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]]]]], ")"]], RowBox[List["1", "-", "\[Beta]"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["a", "+", "b"]], RowBox[List[RowBox[List["-", "b"]], "+", RowBox[List["b", " ", RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]]]]]]]]], ")"]], RowBox[List["-", "\[Beta]"]]], " ", RowBox[List["Sinh", "[", RowBox[List["c", " ", "z"]], "]"]], " ", SqrtBox[RowBox[List[RowBox[List["Cosh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]], "+", RowBox[List["Sinh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]]], RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "\[Beta]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[Beta]"]], ")"]]]]]]]]]]]










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





2002-12-18





© 1998- Wolfram Research, Inc.