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/01.20.21.3742.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18