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 Cosh

 http://functions.wolfram.com/01.20.21.1207.01

 Input Form

 Integrate[E^(p z) Sin[c z]^\[Mu] Cosh[a z], z] == ((1/2) Sin[c z]^\[Mu] ((1/(-a + p - I c \[Mu])) (E^((-a + p) z) Hypergeometric2F1[-((I (-a + p - I c \[Mu]))/(2 c)), -\[Mu], 1 - (I (-a + p - I c \[Mu]))/(2 c), E^(2 I c z)]) + (1/(a + p - I c \[Mu])) (E^((a + p) z) Hypergeometric2F1[ -((I (a + p - I c \[Mu]))/(2 c)), -\[Mu], 1 - (I (a + p - I c \[Mu]))/(2 c), E^(2 I c z)])))/ (1 - E^(2 I c z))^\[Mu]

 Standard Form

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 MathML Form

 p z sin μ ( c z ) cosh ( a z ) z 1 2 ( 1 - 2 c z ) - μ sin μ ( c z ) ( ( p - a ) z - a + p - c μ 2 F 1 ( - ( - a + p - c μ ) 2 c , - μ ; 1 - ( - a + p - c μ ) 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[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "p", "-", RowBox[List["\[ImaginaryI]", " ", "c", " ", "\[Mu]"]]]], ")"]]]], RowBox[List["2", " ", "c"]]]]], Hypergeometric2F1], ",", TagBox[RowBox[List["-", "\[Mu]"]], Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List["1", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "p", "-", RowBox[List["\[ImaginaryI]", " ", "c", " ", "\[Mu]"]]]], ")"]]]], RowBox[List["2", " ", "c"]]]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "c", " ", "z"]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] + ( a + p ) z a + p - c μ 2 F 1 ( - ( a + p - c μ ) 2 c , - μ ; 1 - ( a + p - c μ ) 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[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["a", "+", "p", "-", RowBox[List["\[ImaginaryI]", " ", "c", " ", "\[Mu]"]]]], ")"]]]], RowBox[List["2", " ", "c"]]]]], Hypergeometric2F1], ",", TagBox[RowBox[List["-", "\[Mu]"]], Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List["1", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["a", "+", "p", "-", RowBox[List["\[ImaginaryI]", " ", "c", " ", "\[Mu]"]]]], ")"]]]], RowBox[List["2", " ", "c"]]]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "c", " ", "z"]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] ) z p z c z μ a z 1 2 1 -1 2 c z -1 μ c z μ p -1 a z -1 a p -1 c μ -1 Hypergeometric2F1 -1 -1 a p -1 c μ 2 c -1 -1 μ 1 -1 -1 a p -1 c μ 2 c -1 2 c z a p z a p -1 c μ -1 Hypergeometric2F1 -1 a p -1 c μ 2 c -1 -1 μ 1 -1 a p -1 c μ 2 c -1 2 c z [/itex]

 Rule Form

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

 2002-12-18