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/01.20.21.4095.01

 Input Form

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

 Standard Form

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 MathML Form

 sinh ( z b + e ) cosh v ( z c + f z ) z 2 - v - z b - e ( z b + 2 ( z b + e ) ( b z - 1 ) + 1 ) ( 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]]]]] ( e ( - ( c ( v - 2 s ) - b ) 2 4 f ( v - 2 s ) - 2 e 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 e + f ( v - 2 s ) z + ( 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 ) - - e ( 2 e - ( 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 e + f ( v - 2 s ) z + ( 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 z 1 2 b e z 1 2 c f z v 2 -1 v -1 z 1 2 b -1 e z 1 2 b 2 z 1 2 b e b z 1 2 -1 1 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 e -1 c v -1 2 s -1 b 2 4 f v -1 2 s -1 -1 2 e 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 e f v -1 2 s z 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 e 2 e -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 e f v -1 2 s z 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