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/01.20.21.3806.01

 Input Form

 Integrate[E^(p z) Cos[b z^2] Cosh[c z]^v, z] == (1/b) (I 2^(-2 - v) Sqrt[Pi] Binomial[v, v/2] ((Sqrt[(-I) b] Erfi[(p - 2 I b z)/(2 Sqrt[(-I) b])])/E^((I p^2)/(4 b)) - Sqrt[I b] E^((I p^2)/(4 b)) Erfi[(p + 2 I b z)/(2 Sqrt[I b])]) (1 - Mod[v, 2])) - (1/b) (I 2^(-2 - v) Sqrt[Pi] Sum[Binomial[v, k] (((-Sqrt[(-I) b]) Erfi[(2 c k + p - c v - 2 I b z)/ (2 Sqrt[(-I) b])])/E^((I (2 c k + p - c v)^2)/(4 b)) - (Sqrt[(-I) b] Erfi[(-2 c k + p + c v - 2 I b z)/(2 Sqrt[(-I) b])])/ E^((I (-2 c k + p + c v)^2)/(4 b)) + Sqrt[I b] E^((I (2 c k + p - c v)^2)/(4 b)) Erfi[(2 c k + p - c v + 2 I b z)/ (2 Sqrt[I b])] + Sqrt[I b] E^((I (-2 c k + p + c v)^2)/(4 b)) Erfi[(-2 c k + p + c v + 2 I b z)/(2 Sqrt[I b])]), {k, 0, Floor[(1/2) (-1 + v)]}]) /; Element[v, Integers] && v > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", "z"]]], " ", RowBox[List["Cos", "[", RowBox[List["b", " ", SuperscriptBox["z", "2"]]], "]"]], " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]], "v"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", "b"], RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", "v"]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["p", "2"]]], RowBox[List["4", " ", "b"]]]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["p", "-", 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FractionBox[RowBox[List[RowBox[List["2", " ", "c", " ", "k"]], "+", "p", "-", RowBox[List["c", " ", "v"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", "b"]]]]]], "]"]]]], "+", RowBox[List[SqrtBox[RowBox[List["\[ImaginaryI]", " ", "b"]]], " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "c", " ", "k"]], "+", "p", "+", RowBox[List["c", " ", "v"]]]], ")"]], "2"]]], RowBox[List["4", " ", "b"]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "c", " ", "k"]], "+", "p", "+", RowBox[List["c", " ", "v"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", "b"]]]]]], "]"]]]]]], ")"]]]]]]]], ")"]]]]]]]], "/;", RowBox[List[RowBox[List["v", "\[Element]", "Integers"]], "\[And]", RowBox[List["v", ">", "0"]]]]]]]]

 MathML Form

 p z cos ( b z 2 ) cosh v ( c z ) z 1 b ( 2 - v - 2 π ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox[FractionBox["v", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - b - p 2 4 b erfi ( p - 2 b z 2 - b ) - b p 2 4 b erfi ( p + 2 b z 2 b ) ) ( 1 - v mod 2 \$CellContext`v 2 ) ) - 1 b ( 2 - v - 2 π k = 0 v - 1 2 ( v k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - - b - ( - 2 c k + p + c v ) 2 4 b erfi ( - 2 c k + p + c v - 2 b z 2 - b ) - - b - ( 2 c k + p - c v ) 2 4 b erfi ( 2 c k + p - c v - 2 b z 2 - b ) + b ( - 2 c k + p + c v ) 2 4 b erfi ( - 2 c k + p + c v + 2 b z 2 b ) + b ( 2 c k + p - c v ) 2 4 b erfi ( 2 c k + p - c v + 2 b z 2 b ) ) ) /; v TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] v > 0 Condition z p z b z 2 c z v 1 b -1 2 -1 v -2 1 2 Binomial v v 2 -1 -1 b 1 2 -1 p 2 4 b -1 Erfi p -1 2 b z 2 -1 b 1 2 -1 -1 b 1 2 p 2 4 b -1 Erfi p 2 b z 2 b 1 2 -1 1 -1 \$CellContext`v 2 -1 1 b -1 2 -1 v -2 1 2 k 0 v -1 2 -1 Binomial v k -1 -1 b 1 2 -1 -2 c k p c v 2 4 b -1 Erfi -2 c k p c v -1 2 b z 2 -1 b 1 2 -1 -1 -1 b 1 2 -1 2 c k p -1 c v 2 4 b -1 Erfi 2 c k p -1 c v -1 2 b z 2 -1 b 1 2 -1 b 1 2 -2 c k p c v 2 4 b -1 Erfi -2 c k p c v 2 b z 2 b 1 2 -1 b 1 2 2 c k p -1 c v 2 4 b -1 Erfi 2 c k p -1 c v 2 b z 2 b 1 2 -1 v v 0 [/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_", " ", SuperscriptBox["z_", "2"]]], "]"]], " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List["c_", " ", "z_"]], "]"]], "v_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", "v"]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["p", "2"]]], RowBox[List["4", " ", "b"]]]]]], " ", RowBox[List["Erfi", "[", 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 Date Added to functions.wolfram.com (modification date)

 2002-12-18