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/01.20.21.4616.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18