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/01.20.21.3810.01

 Input Form

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

 Standard Form

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"+", "p", "-", RowBox[List["c", " ", "v"]]]]]]]], "]"]]]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c", " ", "k"]], "+", "p", "-", RowBox[List["c", " ", "v"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "c", " ", "k"]], "+", "p", "+", RowBox[List["c", " ", "v"]]]], ")"]]]], ")"]]]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["v", "\[Element]", "Integers"]], "\[And]", RowBox[List["v", ">", "0"]]]]]]]]

 MathML Form

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

 Rule Form

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

 2002-12-18