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/01.20.21.4105.01

 Input Form

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

 Standard Form

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 MathML Form

 sinh ( b z ) cosh v ( z c + g + f z ) z 2 - v - 2 - b z ( 4 z b + 4 2 b z ( b z - 1 ) + 4 ) ( 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 2 + 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]]]]] ( - g ( v - 2 s ) ( 2 g ( v - 2 s ) - ( c ( v - 2 s ) - b ) 2 4 f ( v - 2 s ) π ( c ( v - 2 s ) - b ) erfi ( - b + c ( v - 2 s ) + 2 f ( v - 2 s ) z 2 f ( v - 2 s ) ) ( f ( v - 2 s ) ) 3 / 2 - 2 2 g ( v - 2 s ) + f z ( v - 2 s ) + ( c ( v - 2 s ) - b ) z f ( v - 2 s ) - 2 ( b - c ( v - 2 s ) ) z - f ( v - 2 s ) z f ( v - 2 s ) - ( b - c ( v - 2 s ) ) 2 4 f ( v - 2 s ) π ( c ( v - 2 s ) - b ) erfi ( - b + c ( v - 2 s ) + 2 f ( v - 2 s ) z 2 - f ( v - 2 s ) ) ( - f ( v - 2 s ) ) 3 / 2 ) - - g ( v - 2 s ) ( 2 g ( v - 2 s ) - ( b + c ( v - 2 s ) ) 2 4 f ( v - 2 s ) π ( b + c ( v - 2 s ) ) erfi ( b + c ( v - 2 s ) + 2 f ( v - 2 s ) z 2 f ( v - 2 s ) ) ( f ( v - 2 s ) ) 3 / 2 - 2 2 g ( v - 2 s ) + f z ( v - 2 s ) + ( b + c ( v - 2 s ) ) z f ( v - 2 s ) - 2 ( - b - c ( v - 2 s ) ) z - f ( v - 2 s ) z f ( v - 2 s ) - ( - b - c ( v - 2 s ) ) 2 4 f ( v - 2 s ) π ( b + c ( v - 2 s ) ) erfi ( b + c ( v - 2 s ) + 2 f ( v - 2 s ) z 2 - f ( v - 2 s ) ) ( - f ( v - 2 s ) ) 3 / 2 ) ) /; v + Condition z b z 1 2 z 1 2 c g f z v 2 -1 v -2 -1 b z 1 2 4 z 1 2 b 4 2 b z 1 2 b z 1 2 -1 4 Binomial v v 2 -1 1 -1 \$CellContext`v 2 b 2 -1 2 -1 v -2 s 0 v -1 2 -1 Binomial v s -1 g v -1 2 s 2 g v -1 2 s -1 c v -1 2 s -1 b 2 4 f v -1 2 s -1 1 2 c v -1 2 s -1 b Erfi -1 b c v -1 2 s 2 f v -1 2 s z 1 2 2 f v -1 2 s 1 2 -1 f v -1 2 s 3 2 -1 -1 2 2 g v -1 2 s f z v -1 2 s c v -1 2 s -1 b z 1 2 f v -1 2 s -1 -1 2 b -1 c v -1 2 s z 1 2 -1 f v -1 2 s z f v -1 2 s -1 -1 b -1 c v -1 2 s 2 4 f v -1 2 s -1 1 2 c v -1 2 s -1 b Erfi -1 b c v -1 2 s 2 f v -1 2 s z 1 2 2 -1 f v -1 2 s 1 2 -1 -1 f v -1 2 s 3 2 -1 -1 -1 g v -1 2 s 2 g v -1 2 s -1 b c v -1 2 s 2 4 f v -1 2 s -1 1 2 b c v -1 2 s Erfi b c v -1 2 s 2 f v -1 2 s z 1 2 2 f v -1 2 s 1 2 -1 f v -1 2 s 3 2 -1 -1 2 2 g v -1 2 s f z v -1 2 s b c v -1 2 s z 1 2 f v -1 2 s -1 -1 2 -1 b -1 c v -1 2 s z 1 2 -1 f v -1 2 s z f v -1 2 s -1 -1 -1 b -1 c v -1 2 s 2 4 f v -1 2 s -1 1 2 b c v -1 2 s Erfi b c v -1 2 s 2 f v -1 2 s z 1 2 2 -1 f v -1 2 s 1 2 -1 -1 f v -1 2 s 3 2 -1 v SuperPlus [/itex]

 Rule Form

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

 2002-12-18