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/01.20.21.1567.01

 Input Form

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

 Standard Form

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 MathML Form

 sinh m ( z b + e + d z ) cosh ( g + f 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]]]]] ( 1 - m mod 2 \$CellContext`m 2 ) sinh ( g + f z ) ( 2 ) m f + 2 - m - 2 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]]]]] ( - g - e ( 2 k - m ) ( 2 ( - 1 ) m 2 ( g + e ( 2 k - m ) ) + ( f + d ( 2 k - m ) ) z + b ( 2 k - m ) z f + d ( 2 k - m ) - ( ( - 1 ) m b 2 ( g + e ( 2 k - m ) ) - b 2 ( 2 k - m ) 2 4 ( f + d ( 2 k - m ) ) ( 2 k - m ) π erfi ( 2 z ( f + d ( 2 k - m ) ) + b ( 2 k - m ) 2 f + d ( 2 k - m ) ) ) / ( f + d ( 2 k - m ) ) 3 / 2 + 2 ( d ( m - 2 k ) - f ) z - b ( 2 k - m ) z d ( m - 2 k ) - f - b - b 2 ( 2 k - m ) 2 4 ( d ( m - 2 k ) - f ) ( 2 k - m ) π erfi ( 2 z ( f + d ( 2 k - m ) ) + b ( 2 k - m ) 2 d ( m - 2 k ) - f ) ( d ( m - 2 k ) - f ) 3 / 2 ) + ( - 1 ) m - g - e ( m - 2 k ) ( 2 ( d ( 2 k - m ) - f ) z - b ( m - 2 k ) z d ( 2 k - m ) - f - b - b 2 ( m - 2 k ) 2 4 ( d ( 2 k - m ) - f ) ( m - 2 k ) π erfi ( b ( m - 2 k ) + 2 ( f + d ( m - 2 k ) ) z 2 d ( 2 k - m ) - f ) ( d ( 2 k - m ) - f ) 3 / 2 + 2 ( - 1 ) m b z ( m - 2 k ) + 2 ( g + e ( m - 2 k ) ) + ( f + d ( m - 2 k ) ) z f + d ( m - 2 k ) - ( ( - 1 ) m b 2 ( g + e ( m - 2 k ) ) - b 2 ( m - 2 k ) 2 4 ( f + d ( m - 2 k ) ) ( m - 2 k ) π erfi ( b ( m - 2 k ) + 2 ( f + d ( m - 2 k ) ) z 2 f + d ( m - 2 k ) ) ) / ( f + d ( m - 2 k ) ) 3 / 2 ) ) /; m + Condition z z 1 2 b e d z m g f z Binomial m m 2 -1 1 -1 \$CellContext`m 2 g f z 2 -1 m f -1 2 -1 m -2 k 0 m -1 2 -1 -1 k Binomial m k -1 g -1 e 2 k -1 m 2 -1 m 2 g e 2 k -1 m f d 2 k -1 m z b 2 k -1 m z 1 2 f d 2 k -1 m -1 -1 -1 m b 2 g e 2 k -1 m -1 b 2 2 k -1 m 2 4 f d 2 k -1 m -1 2 k -1 m 1 2 Erfi 2 z 1 2 f d 2 k -1 m b 2 k -1 m 2 f d 2 k -1 m 1 2 -1 f d 2 k -1 m 3 2 -1 2 d m -1 2 k -1 f z -1 b 2 k -1 m z 1 2 d m -1 2 k -1 f -1 -1 b -1 b 2 2 k -1 m 2 4 d m -1 2 k -1 f -1 2 k -1 m 1 2 Erfi 2 z 1 2 f d 2 k -1 m b 2 k -1 m 2 d m -1 2 k -1 f 1 2 -1 d m -1 2 k -1 f 3 2 -1 -1 m -1 g -1 e m -1 2 k 2 d 2 k -1 m -1 f z -1 b m -1 2 k z 1 2 d 2 k -1 m -1 f -1 -1 b -1 b 2 m -1 2 k 2 4 d 2 k -1 m -1 f -1 m -1 2 k 1 2 Erfi b m -1 2 k 2 f d m -1 2 k z 1 2 2 d 2 k -1 m -1 f 1 2 -1 d 2 k -1 m -1 f 3 2 -1 2 -1 m b z 1 2 m -1 2 k 2 g e m -1 2 k f d m -1 2 k z f d m -1 2 k -1 -1 -1 m b 2 g e m -1 2 k -1 b 2 m -1 2 k 2 4 f d m -1 2 k -1 m -1 2 k 1 2 Erfi b m -1 2 k 2 f d m -1 2 k z 1 2 2 f d m -1 2 k 1 2 -1 f d m -1 2 k 3 2 -1 m SuperPlus [/itex]

 Rule Form

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

 2002-12-18