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 Cosh

 http://functions.wolfram.com/01.20.21.3807.01

 Input Form

 Integrate[E^(p z) Cos[b Sqrt[z]] Cosh[c z]^v, z] == 2^(-2 - v) Binomial[v, v/2] ((4 E^(p z) Cos[b Sqrt[z]])/p + (I b E^(b^2/(4 p)) Sqrt[Pi] Erfi[((-I) b + 2 p Sqrt[z])/(2 Sqrt[p])])/ p^(3/2) - (I b E^(b^2/(4 p)) Sqrt[Pi] Erfi[(I b + 2 p Sqrt[z])/(2 Sqrt[p])])/p^(3/2)) (1 - Mod[v, 2]) + 2^(-2 - v) Sum[Binomial[v, k] (2 ((2 E^((2 c k + p - c v) z) Cos[b Sqrt[z]])/(2 c k + p - c v) + (2 E^((p + c (-2 k + v)) z) Cos[b Sqrt[z]])/(p + c (-2 k + v))) + (I b E^(b^2/(4 (2 c k + p - c v))) Sqrt[Pi] Erfi[((-I) b + 2 (2 c k + p - c v) Sqrt[z])/ (2 Sqrt[2 c k + p - c v])])/(2 c k + p - c v)^(3/2) - (I b E^(b^2/(4 (2 c k + p - c v))) Sqrt[Pi] Erfi[(I b + 2 (2 c k + p - c v) Sqrt[z])/(2 Sqrt[2 c k + p - c v])])/ (2 c k + p - c v)^(3/2) + (I b E^(b^2/(4 (-2 c k + p + c v))) Sqrt[Pi] Erfi[((-I) b + 2 (-2 c k + p + c v) Sqrt[z])/ (2 Sqrt[-2 c k + p + c v])])/(-2 c k + p + c v)^(3/2) - (I b E^(b^2/(4 (p + c (-2 k + v)))) Sqrt[Pi] Erfi[(I b + 2 (p + c (-2 k + v)) Sqrt[z])/ (2 Sqrt[p + c (-2 k + v)])])/(p + c (-2 k + v))^(3/2)), {k, 0, Floor[(1/2) (-1 + v)]}] /; Element[v, Integers] && v > 0

 Standard Form

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"2"]]]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["v", "\[Element]", "Integers"]], "\[And]", RowBox[List["v", ">", "0"]]]]]]]]

 MathML Form

 p z cos ( b z ) cosh v ( c z ) z 2 - v - 2 ( 4 p z cos ( b z ) p + b b 2 4 p 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 ) ( 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 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]]]]] ( 2 ( 2 ( 2 c k + p - c v ) z cos ( b z ) 2 c k + p - c v + 2 ( p + c ( v - 2 k ) ) z cos ( b z ) p + c ( v - 2 k ) ) + b b 2 4 ( - 2 c k + p + c v ) π erfi ( - b + 2 ( - 2 c k + p + c v ) z 2 - 2 c k + p + c v ) ( - 2 c k + p + c v ) 3 / 2 + b b 2 4 ( 2 c k + p - c v ) π erfi ( - b + 2 ( 2 c k + p - c v ) z 2 2 c k + p - c v ) ( 2 c k + p - c v ) 3 / 2 - b b 2 4 ( 2 c k + p - c v ) π erfi ( b + 2 ( 2 c k + p - c v ) z 2 2 c k + p - c v ) ( 2 c k + p - c v ) 3 / 2 - b b 2 4 ( p + c ( v - 2 k ) ) π erfi ( b + 2 ( p + c ( v - 2 k ) ) z 2 p + c ( v - 2 k ) ) ( p + c ( v - 2 k ) ) 3 / 2 ) /; v TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] v > 0 Condition z p z b z 1 2 c z v 2 -1 v -2 4 p z b z 1 2 p -1 b b 2 4 p -1 1 2 Erfi -1 b 2 p z 1 2 2 p 1 2 -1 p 3 2 -1 -1 b b 2 4 p -1 1 2 Erfi b 2 p z 1 2 2 p 1 2 -1 p 3 2 -1 Binomial v v 2 -1 1 -1 \$CellContext`v 2 2 -1 v -2 k 0 v -1 2 -1 Binomial v k 2 2 2 c k p -1 c v z b z 1 2 2 c k p -1 c v -1 2 p c v -1 2 k z b z 1 2 p c v -1 2 k -1 b b 2 4 -2 c k p c v -1 1 2 Erfi -1 b 2 -2 c k p c v z 1 2 2 -2 c k p c v 1 2 -1 -2 c k p c v 3 2 -1 b b 2 4 2 c k p -1 c v -1 1 2 Erfi -1 b 2 2 c k p -1 c v z 1 2 2 2 c k p -1 c v 1 2 -1 2 c k p -1 c v 3 2 -1 -1 b b 2 4 2 c k p -1 c v -1 1 2 Erfi b 2 2 c k p -1 c v z 1 2 2 2 c k p -1 c v 1 2 -1 2 c k p -1 c v 3 2 -1 -1 b b 2 4 p c v -1 2 k -1 1 2 Erfi b 2 p c v -1 2 k z 1 2 2 p c v -1 2 k 1 2 -1 p c v -1 2 k 3 2 -1 v v 0 [/itex]

 Rule Form

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

 2002-12-18