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 Csch

 http://functions.wolfram.com/01.23.21.0254.01

 Input Form

 Integrate[E^(p z) Cos[a z] Cosh[b z] Csch[c z], z] == (-(E^(c z)/2)) (E^(((-I) a - b + p) z) (1/((-I) a - b + p + c)) HypergeometricPFQ[{(c + p - I a - b)/(2 c), 1}, {1 + (c + p - I a - b)/(2 c)}, E^(2 c z)] + E^((I a + b + p) z) (1/(I a + b + p + c)) HypergeometricPFQ[ {(c + p + I a + b)/(2 c), 1}, {(c + p + I a + b)/(2 c) + 1}, E^(2 c z)] + E^(((-I) a + b + p) z) (1/((-I) a + b + p + c)) HypergeometricPFQ[{(c + p - I a + b)/(2 c), 1}, {1 + (c + p - I a + b)/(2 c)}, E^(2 c z)] + E^((I a - b + p) z) (1/(I a - b + p + c)) HypergeometricPFQ[ {(c + p + I a - b)/(2 c), 1}, {1 + (c + p + I a - b)/(2 c)}, E^(2 c z)])

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18