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/01.20.21.4630.01

 Input Form

 Integrate[E^(b z^2 + d z + e) Sinh[a z^2 + p z + q] Cosh[c z^2 + f z + g]^v, z] == (1/((-a + b) (a + b))) (I 2^(-2 - v) Sqrt[Pi] Binomial[v, v/2] ((Sqrt[-a + b] (a + b) Erfi[(d - p - 2 a z + 2 b z)/(2 Sqrt[-a + b])])/ E^(((d - p)^2 - 4 (-a + b) (e + (I Pi)/2 - q))/(4 (-a + b))) + ((-a + b) Sqrt[a + b] Erfi[(d + p + 2 (a + b) z)/(2 Sqrt[a + b])])/ E^(((d + p)^2 - 4 (a + b) (e - (I Pi)/2 + q))/(4 (a + b)))) (1 - Mod[v, 2])) + I 2^(-2 - v) Sqrt[Pi] Sum[Binomial[v, s] (((Sqrt[a + b - c (-2 s + v)] (-a + b + c (-2 s + v)) Erfi[(d + p - f (-2 s + v) + 2 b z - 2 (-a + c (-2 s + v)) z)/ (2 Sqrt[a + b - c (-2 s + v)])])/ E^(((d + p - f (-2 s + v))^2 - 4 (a + b - c (-2 s + v)) (e - (I Pi)/2 + q - g (-2 s + v)))/ (4 (a + b - c (-2 s + v)))) + ((a + b - c (-2 s + v)) Sqrt[-a + b + c (-2 s + v)] Erfi[(d - p + f (-2 s + v) + 2 (-a + b + c (-2 s + v)) z)/(2 Sqrt[-a + b + c (-2 s + v)])])/ E^(((d - p + f (-2 s + v))^2 - 4 (-a + b + c (-2 s + v)) (e + (I Pi)/2 - q + g (-2 s + v)))/ (4 (-a + b + c (-2 s + v)))))/((a + b - c (-2 s + v)) (-a + b + c (-2 s + v))) + ((Sqrt[-a + b - c (-2 s + v)] (a + b + c (-2 s + v)) Erfi[(d - p - f (-2 s + v) + 2 b z - 2 (a + c (-2 s + v)) z)/ (2 Sqrt[-a + b - c (-2 s + v)])])/ E^(((d - p - f (-2 s + v))^2 - 4 (-a + b - c (-2 s + v)) (e + (I Pi)/2 - q - g (-2 s + v)))/ (4 (-a + b - c (-2 s + v)))) + ((-a + b - c (-2 s + v)) Sqrt[a + b + c (-2 s + v)] Erfi[(d + p + f (-2 s + v) + 2 (a + b + c (-2 s + v)) z)/(2 Sqrt[a + b + c (-2 s + v)])])/ E^(((d + p + f (-2 s + v))^2 - 4 (a + b + c (-2 s + v)) (e - (I Pi)/2 + q + g (-2 s + v)))/(4 (a + b + c (-2 s + v)))))/ ((-a + b - c (-2 s + v)) (a + b + c (-2 s + v)))), {s, 0, Floor[(1/2) (-1 + v)]}] /; Element[v, Integers] && v > 0

 Standard Form

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

 MathML Form

 b z 2 + d z + e sinh ( a z 2 + p z + q ) cosh v ( c z 2 + f z + g ) z 2 - v - 2 π ( b - a ) ( a + b ) ( 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 - a ( a + b ) - ( d - p ) 2 - 4 ( b - a ) ( e - q + π 2 ) 4 ( b - a ) erfi ( d - p - 2 a z + 2 b z 2 b - a ) + ( b - a ) a + b - ( d + p ) 2 - 4 ( a + b ) ( e + q - π 2 ) 4 ( a + b ) erfi ( d + p + 2 ( a + b ) z 2 a + b ) ) ( 1 - v mod 2 \$CellContext`v 2 ) + 2 - v - 2 π 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]]]]] ( ( - ( d - p + f ( v - 2 s ) ) 2 - 4 ( - a + b + c ( v - 2 s ) ) ( e - q + g ( v - 2 s ) + π 2 ) 4 ( - a + b + c ( v - 2 s ) ) - a + b + c ( v - 2 s ) ( a + b - c ( v - 2 s ) ) erfi ( d - p + f ( v - 2 s ) + 2 ( - a + b + c ( v - 2 s ) ) z 2 - a + b + c ( v - 2 s ) ) + - ( d + p - f ( v - 2 s ) ) 2 - 4 ( a + b - c ( v - 2 s ) ) ( e + q - g ( v - 2 s ) - π 2 ) 4 ( a + b - c ( v - 2 s ) ) ( - a + b + c ( v - 2 s ) ) a + b - c ( v - 2 s ) erfi ( d + p - f ( v - 2 s ) + 2 b z - 2 ( c ( v - 2 s ) - a ) z 2 a + b - c ( v - 2 s ) ) ) / ( ( a + b - c ( v - 2 s ) ) ( - a + b + c ( v - 2 s ) ) ) + ( - ( d + p + f ( v - 2 s ) ) 2 - 4 ( a + b + c ( v - 2 s ) ) ( e + q + g ( v - 2 s ) - π 2 ) 4 ( a + b + c ( v - 2 s ) ) a + b + c ( v - 2 s ) ( - a + b - c ( v - 2 s ) ) erfi ( d + p + f ( v - 2 s ) + 2 ( a + b + c ( v - 2 s ) ) z 2 a + b + c ( v - 2 s ) ) + - ( d - p - f ( v - 2 s ) ) 2 - 4 ( - a + b - c ( v - 2 s ) ) ( e - q - g ( v - 2 s ) + π 2 ) 4 ( - a + b - c ( v - 2 s ) ) ( a + b + c ( v - 2 s ) ) - a + b - c ( v - 2 s ) erfi ( d - p - f ( v - 2 s ) + 2 b z - 2 ( a + c ( v - 2 s ) ) z 2 - a + b - c ( v - 2 s ) ) ) / ( ( - a + b - c ( v - 2 s ) ) ( a + b + c ( v - 2 s ) ) ) ) /; v + Condition z b z 2 d z e a z 2 p z q c z 2 f z g v 2 -1 v -2 1 2 b -1 a a b -1 Binomial v v 2 -1 b -1 a 1 2 a b -1 d -1 p 2 -1 4 b -1 a e -1 q 2 -1 4 b -1 a -1 Erfi d -1 p -1 2 a z 2 b z 2 b -1 a 1 2 -1 b -1 a a b 1 2 -1 d p 2 -1 4 a b e q -1 2 -1 4 a b -1 Erfi d p 2 a b z 2 a b 1 2 -1 1 -1 \$CellContext`v 2 2 -1 v -2 1 2 s 0 v -1 2 -1 Binomial v s -1 d -1 p f v -1 2 s 2 -1 4 -1 a b c v -1 2 s e -1 q g v -1 2 s 2 -1 4 -1 a b c v -1 2 s -1 -1 a b c v -1 2 s 1 2 a b -1 c v -1 2 s Erfi d -1 p f v -1 2 s 2 -1 a b c v -1 2 s z 2 -1 a b c v -1 2 s 1 2 -1 -1 d p -1 f v -1 2 s 2 -1 4 a b -1 c v -1 2 s e q -1 g v -1 2 s -1 2 -1 4 a b -1 c v -1 2 s -1 -1 a b c v -1 2 s a b -1 c v -1 2 s 1 2 Erfi d p -1 f v -1 2 s 2 b z -1 2 c v -1 2 s -1 a z 2 a b -1 c v -1 2 s 1 2 -1 a b -1 c v -1 2 s -1 a b c v -1 2 s -1 -1 d p f v -1 2 s 2 -1 4 a b c v -1 2 s e q g v -1 2 s -1 2 -1 4 a b c v -1 2 s -1 a b c v -1 2 s 1 2 -1 a b -1 c v -1 2 s Erfi d p f v -1 2 s 2 a b c v -1 2 s z 2 a b c v -1 2 s 1 2 -1 -1 d -1 p -1 f v -1 2 s 2 -1 4 -1 a b -1 c v -1 2 s e -1 q -1 g v -1 2 s 2 -1 4 -1 a b -1 c v -1 2 s -1 a b c v -1 2 s -1 a b -1 c v -1 2 s 1 2 Erfi d -1 p -1 f v -1 2 s 2 b z -1 2 a c v -1 2 s z 2 -1 a b -1 c v -1 2 s 1 2 -1 -1 a b -1 c v -1 2 s a b c v -1 2 s -1 v SuperPlus [/itex]

 Rule Form

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

 2002-12-18