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/01.20.21.3820.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18