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 Cos

 http://functions.wolfram.com/01.07.21.2582.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18