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/01.20.21.4617.01

 Input Form

 Integrate[E^(p z) Sinh[b Sqrt[z]] Cosh[c z]^v, z] == 2^(-2 - v) Binomial[v, v/2] ((4 E^(p z) Sinh[b Sqrt[z]])/p + (b Sqrt[Pi] Erfi[(b - 2 p Sqrt[z])/(2 Sqrt[p])])/ (E^(b^2/(4 p)) p^(3/2)) + (b E^(-(b^2/(4 p)) - I Pi) Sqrt[Pi] Erfi[(b + 2 p Sqrt[z])/(2 Sqrt[p])])/p^(3/2)) (1 - Mod[v, 2]) + 2^(-2 - v) Sum[Binomial[v, s] ((8 E^(p z) Sinh[b Sqrt[z]] (p Cosh[c (2 s - v) z] + c (-2 s + v) Sinh[c (2 s - v) z]))/ ((p + 2 c s - c v) (p + c (-2 s + v))) + (b Sqrt[Pi] Erfi[(-b + 2 (-p + c (-2 s + v)) Sqrt[z])/ (2 Sqrt[p - c (-2 s + v)])])/(E^(b^2/(4 (p - c (-2 s + v)))) (p - c (-2 s + v))^(3/2)) + (b Sqrt[Pi] Erfi[(b + 2 (-p + c (-2 s + v)) Sqrt[z])/ (2 Sqrt[p - c (-2 s + v)])])/(E^(b^2/(4 (p - c (-2 s + v)))) (p - c (-2 s + v))^(3/2)) + (b E^(I Pi - b^2/(4 (p + c (-2 s + v)))) Sqrt[Pi] Erfi[(-b + 2 (p + c (-2 s + v)) Sqrt[z])/ (2 Sqrt[p + c (-2 s + v)])])/(p + c (-2 s + v))^(3/2) + (b E^((-I) Pi - b^2/(4 (p + c (-2 s + v)))) Sqrt[Pi] Erfi[(b + 2 (p + c (-2 s + v)) Sqrt[z])/(2 Sqrt[p + c (-2 s + v)])])/ (p + c (-2 s + v))^(3/2)), {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 ) cosh v ( c z ) z 2 - v - 2 ( b - b 2 4 p - π π erfi ( b + 2 p z 2 p ) p 3 / 2 + b - b 2 4 p π erfi ( b - 2 p z 2 p ) p 3 / 2 + 4 p z sinh ( b z ) p ) ( 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]]]]] ( 1 - v mod 2 \$CellContext`v 2 ) + 2 - v - 2 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 π - b 2 4 ( p + c ( v - 2 s ) ) π erfi ( 2 ( p + c ( v - 2 s ) ) z - b 2 p + c ( v - 2 s ) ) ( p + c ( v - 2 s ) ) 3 / 2 + b - b 2 4 ( p + c ( v - 2 s ) ) - π π erfi ( b + 2 ( p + c ( v - 2 s ) ) z 2 p + c ( v - 2 s ) ) ( p + c ( v - 2 s ) ) 3 / 2 + b - b 2 4 ( p - c ( v - 2 s ) ) π erfi ( 2 ( c ( v - 2 s ) - p ) z - b 2 p - c ( v - 2 s ) ) ( p - c ( v - 2 s ) ) 3 / 2 + b - b 2 4 ( p - c ( v - 2 s ) ) π erfi ( b + 2 ( c ( v - 2 s ) - p ) z 2 p - c ( v - 2 s ) ) ( p - c ( v - 2 s ) ) 3 / 2 + 8 p z sinh ( b z ) ( p cosh ( c ( 2 s - v ) z ) + c ( v - 2 s ) sinh ( c ( 2 s - v ) z ) ) ( p + 2 c s - c v ) ( p + c ( v - 2 s ) ) ) /; v TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] v > 0 Condition z p z b z 1 2 c z v 2 -1 v -2 b -1 b 2 4 p -1 -1 1 2 Erfi b 2 p z 1 2 2 p 1 2 -1 p 3 2 -1 b -1 b 2 4 p -1 1 2 Erfi b -1 2 p z 1 2 2 p 1 2 -1 p 3 2 -1 4 p z b z 1 2 p -1 Binomial v v 2 -1 1 -1 \$CellContext`v 2 2 -1 v -2 s 0 v -1 2 -1 Binomial v s b -1 b 2 4 p c v -1 2 s -1 1 2 Erfi 2 p c v -1 2 s z 1 2 -1 b 2 p c v -1 2 s 1 2 -1 p c v -1 2 s 3 2 -1 b -1 b 2 4 p c v -1 2 s -1 -1 1 2 Erfi b 2 p c v -1 2 s z 1 2 2 p c v -1 2 s 1 2 -1 p c v -1 2 s 3 2 -1 b -1 b 2 4 p -1 c v -1 2 s -1 1 2 Erfi 2 c v -1 2 s -1 p z 1 2 -1 b 2 p -1 c v -1 2 s 1 2 -1 p -1 c v -1 2 s 3 2 -1 b -1 b 2 4 p -1 c v -1 2 s -1 1 2 Erfi b 2 c v -1 2 s -1 p z 1 2 2 p -1 c v -1 2 s 1 2 -1 p -1 c v -1 2 s 3 2 -1 8 p z b z 1 2 p c 2 s -1 v z c v -1 2 s c 2 s -1 v z p 2 c s -1 c v 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