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 Cosh

 http://functions.wolfram.com/01.20.21.1221.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18