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/01.20.21.3812.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

 2002-12-18