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/01.20.21.1213.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", "z"]]], " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["d", "+", RowBox[List["c", " ", "z"]]]], "]"]], "\[Mu]"], RowBox[List["Cosh", "[", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "b"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["d", "+", RowBox[List["c", " ", "z"]]]], ")"]]]]]]], ")"]], RowBox[List["-", "\[Mu]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", RowBox[List["a", "+", "p", "-", RowBox[List["\[ImaginaryI]", " ", "c", " ", "\[Mu]"]]]]], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["2", " ", "b"]], "+", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "p"]], ")"]], " ", "z"]]]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["a", "+", "p", "-", RowBox[List["\[ImaginaryI]", " ", "c", " ", "\[Mu]"]]]], ")"]]]], RowBox[List["2", " ", "c"]]]]], ",", RowBox[List["-", "\[Mu]"]], ",", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["a", "+", "p"]], ")"]]]], "c"], "-", "\[Mu]"]], ")"]]]], ",", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["d", "+", RowBox[List["c", " ", "z"]]]], ")"]]]]]]], "]"]]]], ")"]]]], "-", RowBox[List[FractionBox["1", RowBox[List["a", "-", "p", "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", "\[Mu]"]]]]], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "p"]], ")"]], " ", "z"]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["a", "-", "p", "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", "\[Mu]"]]]], ")"]]]], RowBox[List["2", " ", "c"]]], ",", RowBox[List["-", "\[Mu]"]], ",", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["a", "-", "p"]], ")"]]]], "c"], "-", "\[Mu]"]], ")"]]]], ",", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["d", "+", RowBox[List["c", " ", "z"]]]], ")"]]]]]]], "]"]]]], ")"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["d", "+", RowBox[List["c", " ", "z"]]]], "]"]], "\[Mu]"]]]]]]]

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["p_", " ", "z_"]]], " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["d_", "+", RowBox[List["c_", " ", "z_"]]]], "]"]], "\[Mu]_"], " ", RowBox[List["Cosh", "[", RowBox[List["b_", "+", RowBox[List["a_", " ", "z_"]]]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "b"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["d", "+", RowBox[List["c", " ", "z"]]]], ")"]]]]]]], ")"]], RowBox[List["-", "\[Mu]"]]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["2", " ", "b"]], "+", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "p"]], ")"]], " ", "z"]]]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["a", "+", "p", "-", RowBox[List["\[ImaginaryI]", " ", "c", " ", "\[Mu]"]]]], ")"]]]], RowBox[List["2", " ", "c"]]]]], ",", RowBox[List["-", "\[Mu]"]], ",", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["a", "+", "p"]], ")"]]]], "c"], "-", "\[Mu]"]], ")"]]]], ",", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["d", "+", RowBox[List["c", " ", "z"]]]], ")"]]]]]]], "]"]]]], RowBox[List["a", "+", "p", "-", RowBox[List["\[ImaginaryI]", " ", "c", " ", "\[Mu]"]]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "p"]], ")"]], " ", "z"]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["a", "-", "p", "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", "\[Mu]"]]]], ")"]]]], RowBox[List["2", " ", "c"]]], ",", RowBox[List["-", "\[Mu]"]], ",", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["a", "-", "p"]], ")"]]]], "c"], "-", "\[Mu]"]], ")"]]]], ",", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["d", "+", RowBox[List["c", " ", "z"]]]], ")"]]]]]]], "]"]]]], RowBox[List["a", "-", "p", "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", "\[Mu]"]]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["d", "+", RowBox[List["c", " ", "z"]]]], "]"]], "\[Mu]"]]]]]]]

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

 2002-12-18