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/01.20.21.3926.01

 Input Form

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

 Standard Form

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 MathML Form

 z n p z sin ( b z ) cosh v ( c z ) z 2 - v ( 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 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( - b - p ) z ) - ( b - p ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( b - p ) z ) ) ( 1 - v mod 2 \$CellContext`v 2 ) + 2 - v 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]]]]] ( Γ ( 2 ( n + 1 ) , ( - b - p - 2 c s + c v ) z ) ( - b - p - 2 c s + c v ) - 2 ( n + 1 ) - ( b - p - 2 c s + c v ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( b - p - 2 c s + c v ) z ) + ( - b - p + 2 c s - c v ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( - b - p + 2 c s - c v ) z ) - ( b - p + 2 c s - c v ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( b - p + 2 c s - c v ) z ) ) /; v + n Condition z z n p z 1 2 b z 1 2 c z 1 2 v 2 -1 v Binomial v v 2 -1 b p -2 n 1 Gamma 2 n 1 -1 b -1 p z 1 2 -1 b -1 p -2 n 1 Gamma 2 n 1 b -1 p z 1 2 1 -1 \$CellContext`v 2 2 -1 v s 0 v -1 2 -1 Binomial v s Gamma 2 n 1 -1 b -1 p -1 2 c s c v z 1 2 -1 b -1 p -1 2 c s c v -2 n 1 -1 b -1 p -1 2 c s c v -2 n 1 Gamma 2 n 1 b -1 p -1 2 c s c v z 1 2 -1 b -1 p 2 c s -1 c v -2 n 1 Gamma 2 n 1 -1 b -1 p 2 c s -1 c v z 1 2 -1 b -1 p 2 c s -1 c v -2 n 1 Gamma 2 n 1 b -1 p 2 c s -1 c v z 1 2 v SuperPlus n [/itex]

 Rule Form

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

 2002-12-18