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/01.20.21.4613.01

 Input Form

 Integrate[E^(p Sqrt[z]) Sinh[b Sqrt[z]] Cosh[c z]^v, z] == (1/((b - p)^2 (b + p)^2)) (2^(1 - v) E^(p Sqrt[z]) Binomial[v, v/2] (1 - Mod[v, 2]) (b (2 p + b^2 Sqrt[z] - p^2 Sqrt[z]) Cosh[b Sqrt[z]] + (-p^2 - b^2 (1 + p Sqrt[z]) + p^3 Sqrt[z]) Sinh[b Sqrt[z]])) + 2^(-2 - v) Sum[Binomial[v, s] ((8 E^(p Sqrt[z]) Sinh[b Sqrt[z]] Sinh[c (2 s - v) z])/(c (2 s - v)) + (E^((b^2 + b p + p^2)/(4 c s - 2 c v)) Sqrt[Pi] ((-E^((b^2 + 4 b p + p^2)/(-8 c s + 4 c v))) (b - p) Sqrt[c (2 s - v)] Erfi[(b - p - 2 c (-2 s + v) Sqrt[z])/ (2 Sqrt[c (-2 s + v)])] + E^((3 b^2 + 4 b p + 3 p^2)/ (-8 c s + 4 c v)) ((-(b + p)) Sqrt[c (-2 s + v)] Erfi[(b + p - 2 c (-2 s + v) Sqrt[z])/(2 Sqrt[c (2 s - v)])] + E^((b p)/(2 c s - c v)) (b - p) Sqrt[c (-2 s + v)] Erfi[(b - p + 2 c (-2 s + v) Sqrt[z])/(2 Sqrt[c (2 s - v)])] + E^((b + p)^2/(4 c s - 2 c v)) (b + p) Sqrt[c (2 s - v)] Erfi[(b + p + 2 c (-2 s + v) Sqrt[z])/(2 Sqrt[c (-2 s + v)])])))/ (c (2 s - v) Sqrt[(-c^2) (-2 s + v)^2])), {s, 0, Floor[(1/2) (-1 + v)]}] /; Element[v, Integers] && v > 0

 Standard Form

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"p"]], ")"]], " ", SqrtBox[RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["b", "-", "p", "+", RowBox[List["2", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", "p"]], ")"]], "2"], RowBox[List[RowBox[List["4", " ", "c", " ", "s"]], "-", RowBox[List["2", " ", "c", " ", "v"]]]]]], " ", RowBox[List["(", RowBox[List["b", "+", "p"]], ")"]], " ", SqrtBox[RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["b", "+", "p", "+", 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 MathML Form

 p z sinh ( b z ) cosh v ( c z ) z 1 ( b - p ) 2 ( b + p ) 2 ( 2 1 - v p z ( 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]]]]] ( 1 - v mod 2 \$CellContext`v 2 ) ( b ( z b 2 + 2 p - p 2 z ) cosh ( b z ) + ( z p 3 - p 2 - b 2 ( z p + 1 ) ) sinh ( b z ) ) ) + 2 - v - 2 s = 0 v - 1 2 ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( b 2 + p b + p 2 4 c s - 2 c v π ( 3 b 2 + 4 p b + 3 p 2 4 c v - 8 c s ( b p 2 c s - c v ( b - p ) c ( v - 2 s ) erfi ( b - p + 2 c ( v - 2 s ) z 2 c ( 2 s - v ) ) - ( b + p ) c ( v - 2 s ) erfi ( b + p - 2 c ( v - 2 s ) z 2 c ( 2 s - v ) ) + ( b + p ) 2 4 c s - 2 c v ( b + p ) c ( 2 s - v ) erfi ( b + p + 2 c ( v - 2 s ) z 2 c ( v - 2 s ) ) ) - b 2 + 4 p b + p 2 4 c v - 8 c s ( b - p ) c ( 2 s - v ) erfi ( b - p - 2 c ( v - 2 s ) z 2 c ( v - 2 s ) ) ) ) / ( c ( 2 s - v ) - c 2 ( v - 2 s ) 2 ) + 8 p z sinh ( b z ) sinh ( c ( 2 s - v ) z ) c ( 2 s - v ) ) /; v + Condition z p z 1 2 b z 1 2 c z v 1 b -1 p 2 b p 2 -1 2 1 -1 v p z 1 2 Binomial v v 2 -1 1 -1 \$CellContext`v 2 b z 1 2 b 2 2 p -1 p 2 z 1 2 b z 1 2 z 1 2 p 3 -1 p 2 -1 b 2 z 1 2 p 1 b z 1 2 2 -1 v -2 s 0 v -1 2 -1 Binomial v s b 2 p b p 2 4 c s -1 2 c v -1 1 2 3 b 2 4 p b 3 p 2 4 c v -1 8 c s -1 b p 2 c s -1 c v -1 b -1 p c v -1 2 s 1 2 Erfi b -1 p 2 c v -1 2 s z 1 2 2 c 2 s -1 v 1 2 -1 -1 b p c v -1 2 s 1 2 Erfi b p -1 2 c v -1 2 s z 1 2 2 c 2 s -1 v 1 2 -1 b p 2 4 c s -1 2 c v -1 b p c 2 s -1 v 1 2 Erfi b p 2 c v -1 2 s z 1 2 2 c v -1 2 s 1 2 -1 -1 b 2 4 p b p 2 4 c v -1 8 c s -1 b -1 p c 2 s -1 v 1 2 Erfi b -1 p -1 2 c v -1 2 s z 1 2 2 c v -1 2 s 1 2 -1 c 2 s -1 v -1 c 2 v -1 2 s 2 1 2 -1 8 p z 1 2 b z 1 2 c 2 s -1 v z c 2 s -1 v -1 v SuperPlus [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["p_", " ", SqrtBox["z_"]]]], " ", RowBox[List["Sinh", "[", RowBox[List["b_", " ", SqrtBox["z_"]]], "]"]], " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List["c_", " ", "z_"]], "]"]], "v_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List["1", "-", "v"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", SqrtBox["z"]]]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "p"]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", SqrtBox["z"]]], "-", 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 Date Added to functions.wolfram.com (modification date)

 2002-12-18