html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Cosh

 http://functions.wolfram.com/01.20.21.0853.01

 Input Form

 Integrate[(Cos[e z] Cosh[c z])/(a + b Cos[d z]), z] == (1/4) ((E^((-c + I d - I e) z) ((a + Sqrt[a^2 - b^2]) Hypergeometric2F1[-((I (-c + I d - I e))/d), 1, 2 - (I (-c - I e))/d, (b E^(I d z))/(-a + Sqrt[a^2 - b^2])] + (-a + Sqrt[a^2 - b^2]) Hypergeometric2F1[-((I (-c + I d - I e))/d), 1, 2 - (I (-c - I e))/d, -((b E^(I d z))/(a + Sqrt[a^2 - b^2]))]))/ (b Sqrt[a^2 - b^2] (-c + I d - I e)) + (E^((c + I d - I e) z) ((a + Sqrt[a^2 - b^2]) Hypergeometric2F1[ -((I (c + I d - I e))/d), 1, 2 - (I (c - I e))/d, (b E^(I d z))/(-a + Sqrt[a^2 - b^2])] + (-a + Sqrt[a^2 - b^2]) Hypergeometric2F1[-((I (c + I d - I e))/d), 1, 2 - (I (c - I e))/d, -((b E^(I d z))/(a + Sqrt[a^2 - b^2]))]))/ (b Sqrt[a^2 - b^2] (c + I d - I e)) + (E^((-c + I d + I e) z) ((a + Sqrt[a^2 - b^2]) Hypergeometric2F1[ -((I (-c + I d + I e))/d), 1, 2 - (I (-c + I e))/d, (b E^(I d z))/(-a + Sqrt[a^2 - b^2])] + (-a + Sqrt[a^2 - b^2]) Hypergeometric2F1[-((I (-c + I d + I e))/d), 1, 2 - (I (-c + I e))/d, -((b E^(I d z))/(a + Sqrt[a^2 - b^2]))]))/ (b Sqrt[a^2 - b^2] (-c + I d + I e)) + (E^((c + I d + I e) z) ((a + Sqrt[a^2 - b^2]) Hypergeometric2F1[ -((I (c + I d + I e))/d), 1, 2 - (I (c + I e))/d, (b E^(I d z))/(-a + Sqrt[a^2 - b^2])] + (-a + Sqrt[a^2 - b^2]) Hypergeometric2F1[-((I (c + I d + I e))/d), 1, 2 - (I (c + I e))/d, -((b E^(I d z))/(a + Sqrt[a^2 - b^2]))]))/ (b Sqrt[a^2 - b^2] (c + I d + I e)))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List[RowBox[List["Cos", "[", RowBox[List["e", " ", "z"]], "]"]], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]]]], RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Cos", "[", RowBox[List["d", " ", "z"]], "]"]]]]]]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", "1", ",", RowBox[List["2", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "d", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", "1", ",", RowBox[List["2", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "d", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]]]]]]], "]"]]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List["b", " ", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", "1", ",", RowBox[List["2", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "d", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", "1", ",", RowBox[List["2", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "d", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]]]]]]], "]"]]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List["b", " ", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]], " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", "1", ",", RowBox[List["2", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "d", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", "1", ",", RowBox[List["2", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "d", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]]]]]]], "]"]]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List["b", " ", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", "1", ",", RowBox[List["2", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "d", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", "1", ",", RowBox[List["2", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "d", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]]]]]]], "]"]]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List["b", " ", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]], " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], ")"]]]]]], ")"]]]]]]]]

 MathML Form

 cos ( e z ) cosh ( c z ) a + b cos ( d z ) z 1 4 ( ( ( - c + d + e ) z ( ( a + a 2 - b 2 ) 2 F 1 ( - ( - c + d + e ) d , 1 ; 2 - ( e - c ) d ; b d z a 2 - b 2 - a ) 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["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "d"]], " ", "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], " ", ")"]]]], "d"]]], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List["2", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "e"]], "-", "c"]], ")"]]]], "d"]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "d", " ", "z"]]]]], RowBox[List[SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]], "-", "a"]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] + ( a 2 - b 2 - a ) 2 F 1 ( - ( - c + d + e ) d , 1 ; 2 - ( e - c ) d ; - b d z a + a 2 - b 2 ) 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["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "d"]], " ", "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], " ", ")"]]]], "d"]]], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List["2", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "e"]], "-", "c"]], ")"]]]], "d"]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "d", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] ) ) / ( b a 2 - b 2 ( - c + d + e ) ) + 1 b a 2 - b 2 ( c + d + e ) ( ( c + d + e ) z ( ( a + a 2 - b 2 ) 2 F 1 ( - ( c + d + e ) d , 1 ; 2 - ( c + e ) d ; b d z a 2 - b 2 - a ) 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["c", "+", RowBox[List["\[ImaginaryI]", " ", "d"]], " ", "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], " ", ")"]]]], "d"]]], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List["2", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], " ", ")"]]]], "d"]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "d", " ", "z"]]]]], RowBox[List[SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]], "-", "a"]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] + ( a 2 - b 2 - a ) 2 F 1 ( - ( c + d + e ) d , 1 ; 2 - ( c + e ) d ; - b d z a + a 2 - b 2 ) 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["c", "+", RowBox[List["\[ImaginaryI]", " ", "d"]], " ", "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], " ", ")"]]]], "d"]]], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List["2", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], " ", ")"]]]], "d"]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "d", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] ) ) + ( ( - c - e + d ) z ( ( a + a 2 - b 2 ) 2 F 1 ( - ( - c - e + d ) d , 1 ; 2 - ( - c - e ) d ; b d z a 2 - b 2 - a ) 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["-", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "e"]], "+", RowBox[List["\[ImaginaryI]", " ", "d"]]]], " ", ")"]]]], "d"]]], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List["2", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "d", " ", "z"]]]]], RowBox[List[SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]], "-", "a"]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] + ( a 2 - b 2 - a ) 2 F 1 ( - ( - c - e + d ) d , 1 ; 2 - ( - c - e ) d ; - b d z a + a 2 - b 2 ) 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["-", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "e"]], "+", RowBox[List["\[ImaginaryI]", " ", "d"]]]], " ", ")"]]]], "d"]]], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List["2", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "d", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] ) ) / ( b a 2 - b 2 ( - c - e + d ) ) + 1 b a 2 - b 2 ( c - e + d ) ( ( c - e + d ) z ( ( a + a 2 - b 2 ) 2 F 1 ( - ( c - e + d ) d , 1 ; 2 - ( c - e ) d ; b d z a 2 - b 2 - a ) 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["c", "-", RowBox[List["\[ImaginaryI]", " ", "e"]], "+", RowBox[List["\[ImaginaryI]", " ", "d"]]]], " ", ")"]]]], "d"]]], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List["2", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "d", " ", "z"]]]]], RowBox[List[SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]], "-", "a"]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] + ( a 2 - b 2 - a ) 2 F 1 ( - ( c - e + d ) d , 1 ; 2 - ( c - e ) d ; - b d z a + a 2 - b 2 ) 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["c", "-", RowBox[List["\[ImaginaryI]", " ", "e"]], "+", RowBox[List["\[ImaginaryI]", " ", "d"]]]], " ", ")"]]]], "d"]]], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List["2", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "d", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] ) ) ) z e z c z a b d z -1 1 4 -1 c d e z a a 2 -1 b 2 1 2 Hypergeometric2F1 -1 -1 c d e d -1 1 2 -1 e -1 c d -1 b d z a 2 -1 b 2 1 2 -1 a -1 a 2 -1 b 2 1 2 -1 a Hypergeometric2F1 -1 -1 c d e d -1 1 2 -1 e -1 c d -1 -1 b d z a a 2 -1 b 2 1 2 -1 b a 2 -1 b 2 1 2 -1 c d e -1 1 b a 2 -1 b 2 1 2 c d e -1 c d e z a a 2 -1 b 2 1 2 Hypergeometric2F1 -1 c d e d -1 1 2 -1 c e d -1 b d z a 2 -1 b 2 1 2 -1 a -1 a 2 -1 b 2 1 2 -1 a Hypergeometric2F1 -1 c d e d -1 1 2 -1 c e d -1 -1 b d z a a 2 -1 b 2 1 2 -1 -1 c -1 e d z a a 2 -1 b 2 1 2 Hypergeometric2F1 -1 -1 c -1 e d d -1 1 2 -1 -1 c -1 e d -1 b d z a 2 -1 b 2 1 2 -1 a -1 a 2 -1 b 2 1 2 -1 a Hypergeometric2F1 -1 -1 c -1 e d d -1 1 2 -1 -1 c -1 e d -1 -1 b d z a a 2 -1 b 2 1 2 -1 b a 2 -1 b 2 1 2 -1 c -1 e d -1 1 b a 2 -1 b 2 1 2 c -1 e d -1 c -1 e d z a a 2 -1 b 2 1 2 Hypergeometric2F1 -1 c -1 e d d -1 1 2 -1 c -1 e d -1 b d z a 2 -1 b 2 1 2 -1 a -1 a 2 -1 b 2 1 2 -1 a Hypergeometric2F1 -1 c -1 e d d -1 1 2 -1 c -1 e d -1 -1 b d z a a 2 -1 b 2 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List[RowBox[List["Cos", "[", RowBox[List["e_", " ", "z_"]], "]"]], " ", RowBox[List["Cosh", "[", RowBox[List["c_", " ", "z_"]], "]"]]]], RowBox[List["a_", "+", RowBox[List["b_", " ", RowBox[List["Cos", "[", RowBox[List["d_", " ", "z_"]], "]"]]]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", "1", ",", RowBox[List["2", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "d", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", "1", ",", RowBox[List["2", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "d", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]]]]]]], "]"]]]]]], ")"]]]], RowBox[List["b", " ", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", "1", ",", RowBox[List["2", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "d", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", "1", ",", RowBox[List["2", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "d", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]]]]]]], "]"]]]]]], ")"]]]], RowBox[List["b", " ", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]], " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", "1", ",", RowBox[List["2", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "d", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", "1", ",", RowBox[List["2", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "d", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]]]]]]], "]"]]]]]], ")"]]]], RowBox[List["b", " ", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", "1", ",", RowBox[List["2", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "d", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", "1", ",", RowBox[List["2", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]], "d"]]], ",", RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "d", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]]]]]]], "]"]]]]]], ")"]]]], RowBox[List["b", " ", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]], " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]], ")"]]]]]]], ")"]]]]]]]]

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

 2002-12-18