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/01.20.21.3683.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18