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/01.20.21.3692.01

 Input Form

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

 Standard Form

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 MathML Form

 z α - 1 cos m ( b z r ) cosh v ( c z r + g ) z - 1 r ( 2 - m - v ( k = 0 m - 1 2 ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity, Rule[Editable, True]]], List[TagBox["k", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] s = 0 v - 1 2 ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity, Rule[Editable, True]]], List[TagBox["s", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( 2 g s - g v Γ ( α r , ( - 2 b k + b m - 2 c s + c v ) z r ) ( ( - 2 b k + b m - 2 c s + c v ) z r ) - α r + 2 g s - g v ( ( 2 b k - b m - 2 c s + c v ) z r ) - α r Γ ( α r , ( 2 b k - b m - 2 c s + c v ) z r ) + g v - 2 g s ( ( - 2 b k + b m + 2 c s - c v ) z r ) - α r Γ ( α r , ( - 2 b k + b m + 2 c s - c v ) z r ) + g v - 2 g s ( ( 2 b k - b m + 2 c s - c v ) z r ) - α r Γ ( α r , ( 2 b k - b m + 2 c s - c v ) z r ) ) ) z α ) + 2 - m - v z α ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity, Rule[Editable, True]]], List[TagBox[FractionBox["m", "2"], Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity, Rule[Editable, True]]], List[TagBox[FractionBox["v", "2"], Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( 1 - m mod 2 \$CellContext`m 2 ) ( 1 - v mod 2 \$CellContext`v 2 ) α - 1 r ( 2 - m - v z α ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity, Rule[Editable, True]]], List[TagBox[FractionBox["v", "2"], Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( 1 - v mod 2 \$CellContext`v 2 ) k = 0 m - 1 2 ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity, Rule[Editable, True]]], List[TagBox["k", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( Γ ( α r , ( b m - 2 b k ) z r ) ( ( b m - 2 b k ) z r ) - α r + ( ( 2 b k - b m ) z r ) - α r Γ ( α r , ( 2 b k - b m ) z r ) ) ) - 1 r ( 2 - m - v z α ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity, Rule[Editable, True]]], List[TagBox[FractionBox["m", "2"], Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( 1 - m mod 2 \$CellContext`m 2 ) k = 0 v - 1 2 ( v k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity, Rule[Editable, True]]], List[TagBox["k", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( 2 g k - g v Γ ( α r , ( c v - 2 c k ) z r ) ( ( c v - 2 c k ) z r ) - α r + g v - 2 g k ( ( 2 c k - c v ) z r ) - α r Γ ( α r , ( 2 c k - c v ) z r ) ) ) /; m + v + Condition z z α -1 b z r m c z r g v -1 1 r -1 2 -1 m -1 v k 0 m -1 2 -1 Binomial m k s 0 v -1 2 -1 Binomial v s 2 g s -1 g v Gamma α r -1 -2 b k b m -1 2 c s c v z r -2 b k b m -1 2 c s c v z r -1 α r -1 2 g s -1 g v 2 b k -1 b m -1 2 c s c v z r -1 α r -1 Gamma α r -1 2 b k -1 b m -1 2 c s c v z r g v -1 2 g s -2 b k b m 2 c s -1 c v z r -1 α r -1 Gamma α r -1 -2 b k b m 2 c s -1 c v z r g v -1 2 g s 2 b k -1 b m 2 c s -1 c v z r -1 α r -1 Gamma α r -1 2 b k -1 b m 2 c s -1 c v z r z α 2 -1 m -1 v z α Binomial m m 2 -1 Binomial v v 2 -1 1 -1 \$CellContext`m 2 1 -1 \$CellContext`v 2 α -1 -1 1 r -1 2 -1 m -1 v z α Binomial v v 2 -1 1 -1 \$CellContext`v 2 k 0 m -1 2 -1 Binomial m k Gamma α r -1 b m -1 2 b k z r b m -1 2 b k z r -1 α r -1 2 b k -1 b m z r -1 α r -1 Gamma α r -1 2 b k -1 b m z r -1 1 r -1 2 -1 m -1 v z α Binomial m m 2 -1 1 -1 \$CellContext`m 2 k 0 v -1 2 -1 Binomial v k 2 g k -1 g v Gamma α r -1 c v -1 2 c k z r c v -1 2 c k z r -1 α r -1 g v -1 2 g k 2 c k -1 c v z r -1 α r -1 Gamma α r -1 2 c k -1 c v z r m SuperPlus v SuperPlus [/itex]

 Rule Form

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

 2002-12-18