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 Cot

 http://functions.wolfram.com/01.09.21.0137.01

 Input Form

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

 Standard Form

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 MathML Form

 - ( b + 2 c ) z sin ( a z ) cot ( c z ) z 1 2 ( ( a - b ) z 2 F 1 ( a - b 2 c , 1 ; a - b 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["a", "-", "b"]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List[FractionBox[RowBox[List["a", "-", "b"]], RowBox[List["2", " ", "c"]]], "+", "1"]], 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 - b + ( a - b - 2 c ) z 2 F 1 ( a - b - 2 c 2 c , 1 ; a - b 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[FractionBox[RowBox[List["a", "-", "b", "-", RowBox[List["2", " ", "c"]]]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[FractionBox[RowBox[List["a", "-", "b"]], 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 - b - 2 c + - ( a + b ) z 2 F 1 ( - a + b 2 c , 1 ; - a + b - 2 c 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["a", "+", "b"]], RowBox[List["2", " ", "c"]]]]], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List["-", FractionBox[RowBox[List["a", "+", "b", "-", RowBox[List["2", " ", "c"]]]], 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 + b + - ( a + b + 2 c ) z 2 F 1 ( - a + b + 2 c 2 c , 1 ; - a + b 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["a", "+", "b", "+", RowBox[List["2", " ", "c"]]]], RowBox[List["2", " ", "c"]]]]], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List["-", FractionBox[RowBox[List["a", "+", "b"]], 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 + b + 2 c ) z -1 b 2 c z a z c z 1 2 a -1 b z Hypergeometric2F1 a -1 b 2 c -1 1 a -1 b 2 c -1 1 2 c z a -1 b -1 a -1 b -1 2 c z Hypergeometric2F1 a -1 b -1 2 c 2 c -1 1 a -1 b 2 c -1 2 c z a -1 b -1 2 c -1 -1 a b z Hypergeometric2F1 -1 a b 2 c -1 1 -1 a b -1 2 c 2 c -1 2 c z a b -1 -1 a b 2 c z Hypergeometric2F1 -1 a b 2 c 2 c -1 1 -1 a b 2 c -1 2 c z a b 2 c -1 [/itex]

 Rule Form

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

 2002-12-18