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 Sech

 http://functions.wolfram.com/01.24.21.0203.01

 Input Form

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

 Standard Form

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 MathML Form

 cos ( a z ) sinh ( b z ) sech ( c z ) z 1 2 ( π + ( - b + c - a ) z 2 F 1 ( 1 , - b + c - a 2 c ; - b + 3 c - a 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", " "]]]], 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", " "]]]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] - b + c - a + π + ( - b + c + a ) z 2 F 1 ( 1 , - b + c + a 2 c ; - b + 3 c + a 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", " "]]]], 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", " "]]]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] - b + c + a + ( b + c - a ) z 2 F 1 ( 1 , b + c - a 2 c ; b + 3 c - a 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", " "]]]], 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", " "]]]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] b + c - a + ( b + c + a ) z 2 F 1 ( 1 , b + c + a 2 c ; b + 3 c + a 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", " "]]]], 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", " "]]]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] b + c + a ) z a z b z c z 1 2 -1 b c -1 a z Hypergeometric2F1 1 -1 b c -1 a 2 c -1 -1 b 3 c -1 a 2 c -1 -1 2 c z -1 b c -1 a -1 -1 b c a z Hypergeometric2F1 1 -1 b c a 2 c -1 -1 b 3 c a 2 c -1 -1 2 c z -1 b c a -1 b c -1 a z Hypergeometric2F1 1 b c -1 a 2 c -1 b 3 c -1 a 2 c -1 -1 2 c z b c -1 a -1 b c a z Hypergeometric2F1 1 b c a 2 c -1 b 3 c a 2 c -1 -1 2 c z b c a -1 [/itex]

 Rule Form

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

 2002-12-18