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 Cosh

 http://functions.wolfram.com/01.20.21.1294.01

 Input Form

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

 Standard Form

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RowBox[List["c", "+", "p"]], ")"]], RowBox[List["3", "/", "2"]]]]]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]]]]]]]]

 MathML Form

 p z cos m ( b z ) cosh ( c z ) z ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox[FractionBox["m", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] 2 - m p z ( p cosh ( c z ) - c sinh ( c z ) ) ( 1 - m mod 2 \$CellContext`m 2 ) ( p - c ) ( c + p ) + 2 - m - 1 k = 0 m - 1 2 ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( b b 2 ( m - 2 k ) 2 4 ( p - c ) ( m - 2 k ) π erfi ( 2 ( p - c ) z - b ( m - 2 k ) 2 p - c ) 2 ( p - c ) 3 / 2 + b b 2 ( m - 2 k ) 2 4 ( c + p ) ( m - 2 k ) π erfi ( 2 ( c + p ) z - b ( m - 2 k ) 2 c + p ) 2 ( c + p ) 3 / 2 + ( p - c ) z - b ( m - 2 k ) z p - c + b z ( m - 2 k ) + ( p - c ) z p - c - b b 2 ( m - 2 k ) 2 4 ( p - c ) ( m - 2 k ) π erfi ( b ( m - 2 k ) + 2 ( p - c ) z 2 p - c ) 2 ( p - c ) 3 / 2 + ( c + p ) z - b ( m - 2 k ) z c + p + b z ( m - 2 k ) + ( c + p ) z c + p - b b 2 ( m - 2 k ) 2 4 ( c + p ) ( m - 2 k ) π erfi ( b ( m - 2 k ) + 2 ( c + p ) z 2 c + p ) 2 ( c + p ) 3 / 2 ) /; m + Condition z p z b z 1 2 m c z Binomial m m 2 -1 2 -1 m p z p c z -1 c c z 1 -1 \$CellContext`m 2 p -1 c c p -1 2 -1 m -1 k 0 m -1 2 -1 Binomial m k b b 2 m -1 2 k 2 4 p -1 c -1 m -1 2 k 1 2 Erfi 2 p -1 c z 1 2 -1 b m -1 2 k 2 p -1 c 1 2 -1 2 p -1 c 3 2 -1 b b 2 m -1 2 k 2 4 c p -1 m -1 2 k 1 2 Erfi 2 c p z 1 2 -1 b m -1 2 k 2 c p 1 2 -1 2 c p 3 2 -1 p -1 c z -1 b m -1 2 k z 1 2 p -1 c -1 b z 1 2 m -1 2 k p -1 c z p -1 c -1 -1 b b 2 m -1 2 k 2 4 p -1 c -1 m -1 2 k 1 2 Erfi b m -1 2 k 2 p -1 c z 1 2 2 p -1 c 1 2 -1 2 p -1 c 3 2 -1 c p z -1 b m -1 2 k z 1 2 c p -1 b z 1 2 m -1 2 k c p z c p -1 -1 b b 2 m -1 2 k 2 4 c p -1 m -1 2 k 1 2 Erfi b m -1 2 k 2 c p z 1 2 2 c p 1 2 -1 2 c p 3 2 -1 m SuperPlus [/itex]

 Rule Form

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

 2002-12-18