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/01.20.21.3984.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["z", RowBox[List["\[Alpha]", "-", "1"]]], SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", SuperscriptBox["z", "r"]]]], RowBox[List["Cos", "[", RowBox[List["b", " ", SuperscriptBox["z", "r"]]], "]"]], SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List["c", " ", SuperscriptBox["z", "r"]]], "]"]], "v"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "v"]]], " ", SuperscriptBox["z", "\[Alpha]"], " "]], "r"]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "-", "p"]], ")"]], " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["-", FractionBox["\[Alpha]", "r"]]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["\[Alpha]", "r"], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "-", "p"]], ")"]], " ", SuperscriptBox["z", "r"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "-", "p"]], ")"]], " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["-", FractionBox["\[Alpha]", "r"]]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["\[Alpha]", "r"], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "-", "p"]], ")"]], " ", SuperscriptBox["z", "r"]]]]], "]"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]]]], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "v"]], ")"]]]], "]"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["v", ",", "s"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "-", "p", "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["-", FractionBox["\[Alpha]", "r"]]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["\[Alpha]", "r"], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "-", "p", "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "-", "p", "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["-", FractionBox["\[Alpha]", "r"]]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["\[Alpha]", "r"], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "-", "p", "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "-", "p", "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["-", FractionBox["\[Alpha]", "r"]]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["\[Alpha]", "r"], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "-", "p", "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "-", "p", "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["-", FractionBox["\[Alpha]", "r"]]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["\[Alpha]", "r"], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "-", "p", "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]]]], "]"]]]]]], ")"]]]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["v", "\[Element]", "Integers"]], "\[And]", RowBox[List["v", ">", "0"]]]]]]]]

 MathML Form

 z α - 1 p z r cos ( b z r ) cosh v ( c z r ) z - 2 - v - 1 z α r ( ( 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 , ( - b - p ) z r ) ( ( - b - p ) z r ) - α r + ( ( b - p ) z r ) - α r Γ ( α r , ( b - p ) z r ) ) ( 1 - v mod 2 \$CellContext`v 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 , ( - b - p - 2 c s + c v ) z r ) ( ( - b - p - 2 c s + c v ) z r ) - α r + ( ( b - p - 2 c s + c v ) z r ) - α r Γ ( α r , ( b - p - 2 c s + c v ) z r ) + ( ( - b - p + 2 c s - c v ) z r ) - α r Γ ( α r , ( - b - p + 2 c s - c v ) z r ) + ( ( b - p + 2 c s - c v ) z r ) - α r Γ ( α r , ( b - p + 2 c s - c v ) z r ) ) ) /; v + Condition z z α -1 p z r b z r c z r v -1 2 -1 v -1 z α r -1 Binomial v v 2 -1 Gamma α r -1 -1 b -1 p z r -1 b -1 p z r -1 α r -1 b -1 p z r -1 α r -1 Gamma α r -1 b -1 p z r 1 -1 \$CellContext`v 2 s 0 v -1 2 -1 Binomial v s Gamma α r -1 -1 b -1 p -1 2 c s c v z r -1 b -1 p -1 2 c s c v z r -1 α r -1 b -1 p -1 2 c s c v z r -1 α r -1 Gamma α r -1 b -1 p -1 2 c s c v z r -1 b -1 p 2 c s -1 c v z r -1 α r -1 Gamma α r -1 -1 b -1 p 2 c s -1 c v z r b -1 p 2 c s -1 c v z r -1 α r -1 Gamma α r -1 b -1 p 2 c s -1 c v z r v SuperPlus [/itex]

 Rule Form

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

 2002-12-18