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 Csch

 http://functions.wolfram.com/01.23.21.0248.01

 Input Form

 Integrate[E^(p z) Cos[a z] Sinh[b z] Csch[c z], z] == (E^((I a + b) z) (E^((-I) a z) + E^(I a z)) (-E^((-b) z) + E^(b z)) (1 - E^(2 c z)) ((1/(I a + b - c - p)) (E^(((-I) a - b + c + p) z) Hypergeometric2F1[1, ((-I) a - b + c + p)/(2 c), ((-I) a - b + 3 c + p)/(2 c), E^(2 c z)]) - (1/(I a - b + c + p)) (E^((I a - b + c + p) z) Hypergeometric2F1[1, (I a - b + c + p)/(2 c), (I a - b + 3 c + p)/(2 c), E^(2 c z)]) + I ((E^(((-I) a + b + c + p) z) Hypergeometric2F1[1, ((-I) a + b + c + p)/ (2 c), ((-I) a + b + 3 c + p)/(2 c), E^(2 c z)])/ (a + I (b + c + p)) - (E^((I a + b + c + p) z) Hypergeometric2F1[1, (I a + b + c + p)/(2 c), (I a + b + 3 c + p)/(2 c), E^(2 c z)])/ (a - I (b + c + p)))))/(2 (1 + E^(2 I a z)) (-1 + E^(2 b z)) (-1 + E^(2 c z)))

 Standard Form

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 MathML Form

 p z cos ( a z ) sinh ( b z ) csch ( c z ) z ( b + a ) z ( - a z + a z ) ( - - b z + b z ) ( 1 - 2 c z ) 2 ( 1 + 2 a z ) ( - 1 + 2 b z ) ( - 1 + 2 c z ) ( ( ( b + c - a + p ) z a + ( b + c + p ) 2 F 1 ( 1 , b + c - a + p 2 c ; b + 3 c - a + p 2 c ; 2 c z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["1", Hypergeometric2F1], ",", TagBox[FractionBox[RowBox[List["b", "+", "c", "-", RowBox[List["\[ImaginaryI]", " ", "a"]], " ", "+", "p"]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[FractionBox[RowBox[List["b", "+", RowBox[List["3", " ", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "a"]], " ", "+", "p"]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] - ( b + c + a + p ) z a - ( b + c + p ) 2 F 1 ( 1 , b + c + a + p 2 c ; b + 3 c + a + p 2 c ; 2 c z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["1", Hypergeometric2F1], ",", TagBox[FractionBox[RowBox[List["b", "+", "c", "+", RowBox[List["\[ImaginaryI]", " ", "a"]], " ", "+", "p"]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[FractionBox[RowBox[List["b", "+", RowBox[List["3", " ", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "a"]], " ", "+", "p"]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] ) + ( - b + c - a + p ) z b - c + a - p 2 F 1 ( 1 , - b + c - a + p 2 c ; - b + 3 c - a + p 2 c ; 2 c z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["1", Hypergeometric2F1], ",", TagBox[FractionBox[RowBox[List[RowBox[List["-", "b"]], "+", "c", "-", RowBox[List["\[ImaginaryI]", " ", "a"]], " ", "+", "p"]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[FractionBox[RowBox[List[RowBox[List["-", "b"]], "+", RowBox[List["3", " ", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "a"]], " ", "+", "p"]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] - ( - b + c + a + p ) z - b + c + a + p 2 F 1 ( 1 , - b + c + a + p 2 c ; - b + 3 c + a + p 2 c ; 2 c z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["1", Hypergeometric2F1], ",", TagBox[FractionBox[RowBox[List[RowBox[List["-", "b"]], "+", "c", "+", RowBox[List["\[ImaginaryI]", " ", "a"]], " ", "+", "p"]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[FractionBox[RowBox[List[RowBox[List["-", "b"]], "+", RowBox[List["3", " ", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "a"]], " ", "+", "p"]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] ) z p z a z b z c z b a z -1 a z a z -1 -1 b z b z 1 -1 2 c z 2 1 2 a z -1 2 b z -1 2 c z -1 b c -1 a p z a b c p -1 Hypergeometric2F1 1 b c -1 a p 2 c -1 b 3 c -1 a p 2 c -1 2 c z -1 b c a p z a -1 b c p -1 Hypergeometric2F1 1 b c a p 2 c -1 b 3 c a p 2 c -1 2 c z -1 b c -1 a p z b -1 c a -1 p -1 Hypergeometric2F1 1 -1 b c -1 a p 2 c -1 -1 b 3 c -1 a p 2 c -1 2 c z -1 -1 b c a p z -1 b c a p -1 Hypergeometric2F1 1 -1 b c a p 2 c -1 -1 b 3 c a p 2 c -1 2 c z [/itex]

 Rule Form

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

 2002-12-18