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Csch






Mathematica Notation

Traditional Notation









Elementary Functions > Csch[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic and trigonometric functions > Involving sin and coth > Involving sin(a z)coth(c z) csch( c z)





http://functions.wolfram.com/01.23.21.0217.01









  


  










Input Form





Integrate[Sin[a z] Coth[c z] Csch[c z], z] == (1/((a - I c) ((-I) a + c))) (((I a + c) E^(2 I a z) AppellF1[((-I) a + c)/(2 c), -1, 2, (1/2) (3 - (I a)/c), -E^(-2 c z), E^(-2 c z)] + I (a + I c) AppellF1[(I a + c)/(2 c), -1, 2, (1/2) (3 + (I a)/c), -E^(-2 c z), E^(-2 c z)])/E^((I a + c) z))










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[RowBox[List["Sin", "[", RowBox[List["a_", " ", "z_"]], "]"]], " ", RowBox[List["Coth", "[", RowBox[List["c_", " ", "z_"]], "]"]], " ", RowBox[List["Csch", "[", RowBox[List["c_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "c"]], ")"]]]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "z"]]], " ", RowBox[List["AppellF1", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "c"]], RowBox[List["2", " ", "c"]]], ",", RowBox[List["-", "1"]], ",", "2", ",", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["3", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "a"]], "c"]]], ")"]]]], ",", RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", "c", " ", "z"]]]]], ",", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", "c", " ", "z"]]]]], "]"]]]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", RowBox[List["AppellF1", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "c"]], RowBox[List["2", " ", "c"]]], ",", RowBox[List["-", "1"]], ",", "2", ",", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["3", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "a"]], "c"]]], ")"]]]], ",", RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", "c", " ", "z"]]]]], ",", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", "c", " ", "z"]]]]], "]"]]]]]], ")"]]]], RowBox[List[RowBox[List["(", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "c"]], ")"]]]]]]]]]










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





2002-12-18





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