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/01.20.21.4185.01

 Input Form

 Integrate[Sinh[b Sqrt[z]]^m Cosh[c Sqrt[z] + g]^v, z] == (2^(-m - v) z Binomial[m, m/2] Binomial[v, v/2] (1 - Mod[m, 2]) (1 - Mod[v, 2]))/I^m - (1/c^2) ((2^(2 - m - v) Binomial[m, m/2] (1 - Mod[m, 2]) Sum[(1/(-2 s + v)^2) (Binomial[v, s] (Cosh[(2 s - v) (g + c Sqrt[z])] + c (-2 s + v) Sqrt[z] Sinh[(2 s - v) (g + c Sqrt[z])])), {s, 0, Floor[(1/2) (-1 + v)]}])/ I^m) - (1/b^2) ((2^(2 - m - v) Binomial[v, v/2] (1 - Mod[v, 2]) Sum[(1/(-2 k + m)^2) ((-1)^k Binomial[m, k] (Cosh[-((I m Pi)/2) + b (2 k - m) Sqrt[z]] - b (2 k - m) Sqrt[z] Sinh[-((I m Pi)/2) + b (2 k - m) Sqrt[z]])), {k, 0, Floor[(1/2) (-1 + m)]}])/I^m) - (2^(2 - m - v) Sum[(-1)^k Binomial[m, k] Sum[Binomial[v, s] ((Cosh[-((I m Pi)/2) + 2 g s - g v + (2 b k - b m + 2 c s - c v) Sqrt[z]] - (2 b k - b m + 2 c s - c v) Sqrt[z] Sinh[-((I m Pi)/2) + 2 g s - g v + (2 b k - b m + 2 c s - c v) Sqrt[z]])/ (2 b k - b m + 2 c s - c v)^2 + (Cosh[-((I m Pi)/2) - 2 g s + g v + (2 b k - b m - 2 c s + c v) Sqrt[z]] - (2 b k - b m - 2 c s + c v) Sqrt[z] Sinh[-((I m Pi)/2) - 2 g s + g v + (2 b k - b m - 2 c s + c v) Sqrt[z]])/(2 b k - b m - 2 c s + c v)^2), {s, 0, Floor[(1/2) (-1 + v)]}], {k, 0, Floor[(1/2) (-1 + m)]}])/ I^m /; Element[m, Integers] && m > 0 && Element[v, Integers] && v > 0

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18