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/01.20.21.4852.01

 Input Form

 Integrate[z^(\[Alpha] - 1) E^(p z^r) Sinh[b z^r]^m Cosh[c z^r]^v, z] == ((2^(-m - v) z^\[Alpha])/r) (((-I^m) Binomial[m, m/2] Binomial[v, v/2] Gamma[\[Alpha]/r, (-p) z^r] (-1 + Mod[m, 2]) (-1 + Mod[v, 2]))/ ((-p) z^r)^(\[Alpha]/r) + Binomial[v, v/2] (-1 + Mod[v, 2]) Sum[(-1)^k Binomial[m, k] (Gamma[\[Alpha]/r, (2 b k - b m - p) z^r]/ ((2 b k - b m - p) z^r)^(\[Alpha]/r) + ((-1)^m Gamma[\[Alpha]/r, (-(2 b k - b m + p)) z^r])/ ((-(2 b k - b m + p)) z^r)^(\[Alpha]/r)), {k, 0, Floor[(1/2) (-1 + m)]}] + I^m Binomial[m, m/2] (-1 + Mod[m, 2]) Sum[Binomial[v, s] (Gamma[\[Alpha]/r, (-(p + 2 c s - c v)) z^r]/ ((-(p + 2 c s - c v)) z^r)^(\[Alpha]/r) + Gamma[\[Alpha]/r, (-(p + c (-2 s + v))) z^r]/ ((-(p + c (-2 s + v))) z^r)^(\[Alpha]/r)), {s, 0, Floor[(1/2) (-1 + v)]}] + Sum[(-1)^k Binomial[m, k] Sum[Binomial[v, s] ((-((2 b k - b m - p + 2 c s - c v) z^r)^(-(\[Alpha]/r))) Gamma[\[Alpha]/r, (2 b k - b m - p + 2 c s - c v) z^r] - Gamma[\[Alpha]/r, (2 b k - b m - p - 2 c s + c v) z^r]/ ((2 b k - b m - p - 2 c s + c v) z^r)^(\[Alpha]/r) + E^(I m Pi) ((-((-2 b k + b m - p - 2 c s + c v) z^r)^ (-(\[Alpha]/r))) Gamma[\[Alpha]/r, (-2 b k + b m - p - 2 c s + c v) z^r] - Gamma[\[Alpha]/r, (-(2 b k - b m + p - 2 c s + c v)) z^r]/((-(2 b k - b m + p - 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 p z r sinh m ( b z r ) cosh v ( c z r ) z 2 - m - v z α r ( - m ( - p z r ) - α r ( 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]]]]] Γ ( α r , - p z r ) ( m mod 2 \$CellContext`m 2 - 1 ) ( v mod 2 \$CellContext`v 2 - 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]]]]] ( v mod 2 \$CellContext`v 2 - 1 ) 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]]]]] ( Γ ( α r , ( 2 b k - b m - p ) z r ) ( ( 2 b k - b m - p ) z r ) - α r + ( - 1 ) m ( - ( 2 b k - b m + p ) z r ) - α r Γ ( α r , - ( 2 b k - b m + p ) z r ) ) + 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]]]]] ( m mod 2 \$CellContext`m 2 - 1 ) 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]]]]] ( Γ ( α r , - ( p + 2 c s - c v ) z r ) ( - ( p + 2 c s - c v ) z r ) - α r + ( - ( p + c ( v - 2 s ) ) z r ) - α r Γ ( α r , - ( p + c ( v - 2 s ) ) z r ) ) + 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]]]]] ( - Γ ( α r , ( 2 b k - b m - p - 2 c s + c v ) z r ) ( ( 2 b k - b m - p - 2 c s + c v ) z r ) - α r + m π ( - ( ( - 2 b k + b m - p - 2 c s + c v ) z r ) - α r Γ ( α r , ( - 2 b k + b m - p - 2 c s + c v ) z r ) - ( - ( 2 b k - b m + p - 2 c s + c v ) z r ) - α r Γ ( α r , - ( 2 b k - b m + p - 2 c s + c v ) z r ) ) - ( ( 2 b k - b m - p + 2 c s - c v ) z r ) - α r Γ ( α r , ( 2 b k - b m - p + 2 c s - c v ) z r ) ) ) /; m + v + Condition z z α -1 p z r b z r m c z r v 2 -1 m -1 v z α r -1 -1 m -1 p z r -1 α r -1 Binomial m m 2 -1 Binomial v v 2 -1 Gamma α r -1 -1 p z r \$CellContext`m 2 -1 \$CellContext`v 2 -1 Binomial v v 2 -1 \$CellContext`v 2 -1 k 0 m -1 2 -1 -1 k Binomial m k Gamma α r -1 2 b k -1 b m -1 p z r 2 b k -1 b m -1 p z r -1 α r -1 -1 m -1 2 b k -1 b m p z r -1 α r -1 Gamma α r -1 -1 2 b k -1 b m p z r m Binomial m m 2 -1 \$CellContext`m 2 -1 s 0 v -1 2 -1 Binomial v s Gamma α r -1 -1 p 2 c s -1 c v z r -1 p 2 c s -1 c v z r -1 α r -1 -1 p c v -1 2 s z r -1 α r -1 Gamma α r -1 -1 p c v -1 2 s z r k 0 m -1 2 -1 -1 k Binomial m k s 0 v -1 2 -1 Binomial v s -1 Gamma α r -1 2 b k -1 b m -1 p -1 2 c s c v z r 2 b k -1 b m -1 p -1 2 c s c v z r -1 α r -1 m -1 -2 b k b m -1 p -1 2 c s c v z r -1 α r -1 Gamma α r -1 -2 b k b m -1 p -1 2 c s c v z r -1 -1 2 b k -1 b m p -1 2 c s c v z r -1 α r -1 Gamma α r -1 -1 2 b k -1 b m p -1 2 c s c v z r -1 2 b k -1 b m -1 p 2 c s -1 c v z r -1 α r -1 Gamma α r -1 2 b k -1 b m -1 p 2 c s -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