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 Csc

 http://functions.wolfram.com/01.10.21.0061.01

 Input Form

 Integrate[E^(p z) Cos[b z] Csc[c z], z] == (1/2) (1 - E^(2 I c z)) Csc[c z] ((1/((-I) b + I c + p)) (E^(((-I) b + p) z) HypergeometricPFQ[ {1, 1/2 - b/(2 c) - (I p)/(2 c)}, {3/2 - b/(2 c) - (I p)/(2 c)}, E^(2 I c z)]) + (1/(I b + I c + p)) (E^((I b + p) z) HypergeometricPFQ[{1, 1/2 + b/(2 c) - (I p)/(2 c)}, {3/2 + b/(2 c) - (I p)/(2 c)}, E^(2 I c z)]))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", "z"]]], RowBox[List["Cos", "[", RowBox[List["b", " ", "z"]], "]"]], RowBox[List["Csc", "[", RowBox[List["c", " ", "z"]], "]"]], " ", RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "c", " ", "z"]]]]], ")"]], " ", RowBox[List["Csc", "[", RowBox[List["c", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", RowBox[List["\[ImaginaryI]", " ", "c"]], "+", "p"]]], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", "p"]], ")"]], " ", "z"]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", RowBox[List[FractionBox["1", "2"], "-", FractionBox["b", RowBox[List["2", " ", "c"]]], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "p"]], RowBox[List["2", " ", "c"]]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], "-", FractionBox["b", RowBox[List["2", " ", "c"]]], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "p"]], RowBox[List["2", " ", "c"]]]]], "}"]], ",", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "c", " ", "z"]]]]], "]"]]]], ")"]]]], "+", RowBox[List[FractionBox["1", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["\[ImaginaryI]", " ", "c"]], "+", "p"]]], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", "p"]], ")"]], " ", "z"]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", RowBox[List[FractionBox["1", "2"], "+", FractionBox["b", RowBox[List["2", " ", "c"]]], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "p"]], RowBox[List["2", " ", "c"]]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], "+", FractionBox["b", RowBox[List["2", " ", "c"]]], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "p"]], RowBox[List["2", " ", "c"]]]]], "}"]], ",", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "c", " ", "z"]]]]], "]"]]]], ")"]]]]]], ")"]]]]]]]]

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["p_", " ", "z_"]]], " ", RowBox[List["Cos", "[", RowBox[List["b_", " ", "z_"]], "]"]], " ", RowBox[List["Csc", "[", RowBox[List["c_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "c", " ", "z"]]]]], ")"]], " ", RowBox[List["Csc", "[", RowBox[List["c", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", "p"]], ")"]], " ", "z"]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", RowBox[List[FractionBox["1", "2"], "-", FractionBox["b", RowBox[List["2", " ", "c"]]], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "p"]], RowBox[List["2", " ", "c"]]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], "-", FractionBox["b", RowBox[List["2", " ", "c"]]], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "p"]], RowBox[List["2", " ", "c"]]]]], "}"]], ",", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "c", " ", "z"]]]]], "]"]]]], RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", RowBox[List["\[ImaginaryI]", " ", "c"]], "+", "p"]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", "p"]], ")"]], " ", "z"]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", RowBox[List[FractionBox["1", "2"], "+", FractionBox["b", RowBox[List["2", " ", "c"]]], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "p"]], RowBox[List["2", " ", "c"]]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], "+", FractionBox["b", RowBox[List["2", " ", "c"]]], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "p"]], RowBox[List["2", " ", "c"]]]]], "}"]], ",", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "c", " ", "z"]]]]], "]"]]]], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["\[ImaginaryI]", " ", "c"]], "+", "p"]]]]], ")"]]]]]]]]

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

 2002-12-18