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/01.20.21.3816.01

 Input Form

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

 Standard Form

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"v"]]]], ")"]], "2"]]], ")"]], "2"]]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["v", "\[Element]", "Integers"]], "\[And]", RowBox[List["v", ">", "0"]]]]]]]]

 MathML Form

 p z cos ( b z ) cosh v ( c z ) z 1 ( b 2 + p 2 ) 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 ) ( ( ( z p + 1 ) b 2 + p 2 ( p z - 1 ) ) cos ( b z ) + b ( z b 2 - 2 p + p 2 z ) sin ( b z ) ) ) + 2 1 - v p z 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]]]]] ( ( ( p 2 ( p z - 1 ) - ( - b - 2 c s + c v ) 2 ( z p + 1 ) ) cosh ( ( - b - 2 c s + c v ) z ) - ( - b - 2 c s + c v ) ( z p 2 - 2 p - ( - b - 2 c s + c v ) 2 z ) sinh ( ( - b - 2 c s + c v ) z ) ) / ( p 2 - ( - b - 2 c s + c v ) 2 ) 2 + ( ( p 2 ( p z - 1 ) - ( - b + 2 c s - c v ) 2 ( z p + 1 ) ) cosh ( ( - b + 2 c s - c v ) z ) - ( - b + 2 c s - c v ) ( z p 2 - 2 p - ( - b + 2 c s - c v ) 2 z ) sinh ( ( - b + 2 c s - c v ) z ) ) / ( p 2 - ( - b + 2 c s - c v ) 2 ) 2 ) /; v + Condition z p z 1 2 b z 1 2 c z 1 2 v 1 b 2 p 2 2 -1 2 1 -1 v p z 1 2 Binomial v v 2 -1 1 -1 \$CellContext`v 2 z 1 2 p 1 b 2 p 2 p z 1 2 -1 b z 1 2 b z 1 2 b 2 -1 2 p p 2 z 1 2 b z 1 2 2 1 -1 v p z 1 2 s 0 v -1 2 -1 Binomial v s p 2 p z 1 2 -1 -1 -1 b -1 2 c s c v 2 z 1 2 p 1 -1 b -1 2 c s c v z 1 2 -1 -1 b -1 2 c s c v z 1 2 p 2 -1 2 p -1 -1 b -1 2 c s c v 2 z 1 2 -1 b -1 2 c s c v z 1 2 p 2 -1 -1 b -1 2 c s c v 2 2 -1 p 2 p z 1 2 -1 -1 -1 b 2 c s -1 c v 2 z 1 2 p 1 -1 b 2 c s -1 c v z 1 2 -1 -1 b 2 c s -1 c v z 1 2 p 2 -1 2 p -1 -1 b 2 c s -1 c v 2 z 1 2 -1 b 2 c s -1 c v z 1 2 p 2 -1 -1 b 2 c s -1 c v 2 2 -1 v SuperPlus [/itex]

 Rule Form

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

 2002-12-18