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/01.20.21.0845.01

 Input Form

 Integrate[Cos[b z^2 + d z + e]^m Cosh[c z^2 + f z + g], z] == -((1/c) ((2^(-2 - m) Sqrt[Pi] Binomial[m, m/2] (Sqrt[-c] E^(f^2/(2 c)) Erfi[(Sqrt[-c] (f + 2 c z))/(2 c)] - Sqrt[c] E^(2 g) Erfi[(f + 2 c z)/(2 Sqrt[c])]) (1 - Mod[m, 2]))/ E^((f^2 + 4 c g)/(4 c)))) + 2^(-2 - m) Sqrt[Pi] Sum[Binomial[m, k] (-((E^(-g + I e (2 k - m) - (f - 2 I d k + I d m)^2/(-4 c + 8 I b k - 4 I b m)) Sqrt[-c + 2 I b k - I b m] Erfi[(-f - 2 c z + 2 k (I d + 2 I b z) - m (I d + 2 I b z))/ (2 Sqrt[-c + 2 I b k - I b m])])/(c + I b (-2 k + m))) + (E^(g - 2 I e m + I e (-2 k + m) - (f + 2 I d k - I d m)^2/ (4 c + 8 I b k - 4 I b m)) ((-E^(4 I e k)) Sqrt[c + 2 I b k - I b m] Erfi[(f + 2 c z + 2 k (I d + 2 I b z) - m (I d + 2 I b z))/(2 Sqrt[c + 2 I b k - I b m])] + E^(2 (-g + I e m + (f + 2 I d k - I d m)^2/(4 c + 8 I b k - 4 I b m))) Sqrt[-c - 2 I b k + I b m] Erfi[(-f - 2 c z - 2 k (I d + 2 I b z) + m (I d + 2 I b z))/ (2 Sqrt[-c - 2 I b k + I b m])]))/(-c - 2 I b k + I b m) + (E^(g + I e (-2 k + m) + (f - 2 I d k + I d m)^2/(-4 c + 8 I b k - 4 I b m)) Erfi[(f + 2 c z - 2 k (I d + 2 I b z) + m (I d + 2 I b z))/(2 Sqrt[c + I b (-2 k + m)])])/ Sqrt[c + I b (-2 k + m)]), {k, 0, Floor[(1/2) (-1 + m)]}] /; Element[m, Integers] && m > 0

 Standard Form

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 MathML Form

 cos m ( b z 2 + d z + e ) cosh ( c z 2 + f z + g ) z 2 - m - 2 π 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]]]]] ( 1 - c - 2 b k + b m ( - ( f + 2 d k - d m ) 2 4 c + 8 b k - 4 b m + g - 2 e m + e ( m - 2 k ) ( 2 ( ( f + 2 d k - d m ) 2 4 c + 8 b k - 4 b m - g + e m ) - c - 2 b k + b m erfi ( - f - 2 c z - 2 k ( d + 2 b z ) + m ( d + 2 b z ) 2 - c - 2 b k + b m ) - 4 e k c + 2 b k - b m erfi ( f + 2 c z + 2 k ( d + 2 b z ) - m ( d + 2 b z ) 2 c + 2 b k - b m ) ) ) + ( f - 2 d k + d m ) 2 - 4 c + 8 b k - 4 b m + g + e ( m - 2 k ) erfi ( f + 2 c z - 2 k ( d + 2 b z ) + m ( d + 2 b z ) 2 c + b ( m - 2 k ) ) c + b ( m - 2 k ) - 1 c + b ( m - 2 k ) ( - ( f - 2 d k + d m ) 2 - 4 c + 8 b k - 4 b m - g + e ( 2 k - m ) - c + 2 b k - b m erfi ( - f - 2 c z + 2 k ( d + 2 b z ) - m ( d + 2 b z ) 2 - c + 2 b k - b m ) ) ) - 1 c ( 2 - m - 2 - f 2 + 4 c g 4 c π ( 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 f 2 2 c erfi ( - c ( f + 2 c z ) 2 c ) - c 2 g erfi ( f + 2 c z 2 c ) ) ( 1 - m mod 2 \$CellContext`m 2 ) ) /; m + Condition z b z 2 d z e m c z 2 f z g 2 -1 m -2 1 2 k 0 m -1 2 -1 Binomial m k 1 -1 c -1 2 b k b m -1 -1 f 2 d k -1 d m 2 4 c 8 b k -1 4 b m -1 g -1 2 e m e m -1 2 k 2 f 2 d k -1 d m 2 4 c 8 b k -1 4 b m -1 -1 g e m -1 c -1 2 b k b m 1 2 Erfi -1 f -1 2 c z -1 2 k d 2 b z m d 2 b z 2 -1 c -1 2 b k b m 1 2 -1 -1 4 e k c 2 b k -1 b m 1 2 Erfi f 2 c z 2 k d 2 b z -1 m d 2 b z 2 c 2 b k -1 b m 1 2 -1 f -1 2 d k d m 2 -4 c 8 b k -1 4 b m -1 g e m -1 2 k Erfi f 2 c z -1 2 k d 2 b z m d 2 b z 2 c b m -1 2 k 1 2 -1 c b m -1 2 k 1 2 -1 -1 1 c b m -1 2 k -1 -1 f -1 2 d k d m 2 -4 c 8 b k -1 4 b m -1 -1 g e 2 k -1 m -1 c 2 b k -1 b m 1 2 Erfi -1 f -1 2 c z 2 k d 2 b z -1 m d 2 b z 2 -1 c 2 b k -1 b m 1 2 -1 -1 1 c -1 2 -1 m -2 -1 f 2 4 c g 4 c -1 1 2 Binomial m m 2 -1 -1 c 1 2 f 2 2 c -1 Erfi -1 c 1 2 f 2 c z 2 c -1 -1 c 1 2 2 g Erfi f 2 c z 2 c 1 2 -1 1 -1 \$CellContext`m 2 m SuperPlus [/itex]

 Rule Form

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

 2002-12-18