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/01.20.21.1555.01

 Input Form

 Integrate[Sinh[b Sqrt[z] + e]^m Cosh[c z], z] == ((I/2)^m Binomial[m, m/2] (1 - Mod[m, 2]) Sinh[c z])/c + 2^(-2 - m) Sum[(-1)^k Binomial[m, k] ((-((2 E^((-b) (2 k - m) Sqrt[z] - c z))/c) + (2 (-1)^m E^(2 e (2 k - m) + b (2 k - m) Sqrt[z] + c z))/c - (b E^((b^2 (2 k - m)^2)/(4 c)) (2 k - m) Sqrt[Pi] Erfi[(b (2 k - m) + 2 c Sqrt[z])/(2 Sqrt[-c])])/(-c)^(3/2) - (1/c^(3/2)) ((-1)^m b E^(2 e (2 k - m) - (b^2 (2 k - m)^2)/(4 c)) (2 k - m) Sqrt[Pi] Erfi[(b (2 k - m) + 2 c Sqrt[z])/(2 Sqrt[c])]))/ E^(e (2 k - m)) + ((-1)^m (-((2 E^((-b) (-2 k + m) Sqrt[z] - c z))/ c) + (2 (-1)^m E^(2 e (-2 k + m) + b (-2 k + m) Sqrt[z] + c z))/ c - (b E^((b^2 (-2 k + m)^2)/(4 c)) (-2 k + m) Sqrt[Pi] Erfi[(b (-2 k + m) + 2 c Sqrt[z])/(2 Sqrt[-c])])/(-c)^(3/2) - (1/c^(3/2)) ((-1)^m b E^(-((b^2 (-2 k + m)^2)/(4 c)) + 2 e (-2 k + m)) (-2 k + m) Sqrt[Pi] Erfi[(b (-2 k + m) + 2 c Sqrt[z])/(2 Sqrt[c])])))/ E^(e (-2 k + m))), {k, 0, Floor[(1/2) (-1 + m)]}] /; Element[m, Integers] && m > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List[RowBox[List["b", " ", SqrtBox["z"]]], "+", "e"]], "]"]], "m"], RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["\[ImaginaryI]", "2"], ")"]], "m"], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["c", " ", "z"]], "]"]]]], "c"], "+", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", "m"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]]]], 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FractionBox[RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]], "2"]]], RowBox[List["4", " ", "c"]]]]], "+", RowBox[List["2", " ", "e", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["2", " ", "c", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["c"]]]], "]"]]]], ")"]]]], ")"]]]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]]]]]]]]

 MathML Form

 sinh m ( z b + e ) cosh ( c z ) 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]]]]] ( 1 - m mod 2 \$CellContext`m 2 ) sinh ( c z ) ( 2 ) m c + 2 - m - 2 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]]]]] ( - e ( 2 k - m ) ( - b b 2 ( 2 k - m ) 2 4 c ( 2 k - m ) π erfi ( 2 z c + b ( 2 k - m ) 2 - c ) ( - c ) 3 / 2 - ( - 1 ) m b 2 e ( 2 k - m ) - b 2 ( 2 k - m ) 2 4 c ( 2 k - m ) π erfi ( 2 z c + b ( 2 k - m ) 2 c ) c 3 / 2 + 2 ( - 1 ) m 2 e ( 2 k - m ) + b z ( 2 k - m ) + c z c - 2 - b z ( 2 k - m ) - c z c ) + ( - 1 ) m - e ( m - 2 k ) ( - b b 2 ( m - 2 k ) 2 4 c ( m - 2 k ) π erfi ( 2 z c + b ( m - 2 k ) 2 - c ) ( - c ) 3 / 2 - ( - 1 ) m b 2 e ( m - 2 k ) - b 2 ( m - 2 k ) 2 4 c ( m - 2 k ) π erfi ( 2 z c + b ( m - 2 k ) 2 c ) c 3 / 2 + 2 ( - 1 ) m 2 e ( m - 2 k ) + b z ( m - 2 k ) + c z c - 2 - b z ( m - 2 k ) - c z c ) ) /; m + Condition z z 1 2 b e m c z Binomial m m 2 -1 1 -1 \$CellContext`m 2 c z 2 -1 m c -1 2 -1 m -2 k 0 m -1 2 -1 -1 k Binomial m k -1 e 2 k -1 m -1 b b 2 2 k -1 m 2 4 c -1 2 k -1 m 1 2 Erfi 2 z 1 2 c b 2 k -1 m 2 -1 c 1 2 -1 -1 c 3 2 -1 -1 -1 m b 2 e 2 k -1 m -1 b 2 2 k -1 m 2 4 c -1 2 k -1 m 1 2 Erfi 2 z 1 2 c b 2 k -1 m 2 c 1 2 -1 c 3 2 -1 2 -1 m 2 e 2 k -1 m b z 1 2 2 k -1 m c z c -1 -1 2 -1 b z 1 2 2 k -1 m -1 c z c -1 -1 m -1 e m -1 2 k -1 b b 2 m -1 2 k 2 4 c -1 m -1 2 k 1 2 Erfi 2 z 1 2 c b m -1 2 k 2 -1 c 1 2 -1 -1 c 3 2 -1 -1 -1 m b 2 e m -1 2 k -1 b 2 m -1 2 k 2 4 c -1 m -1 2 k 1 2 Erfi 2 z 1 2 c b m -1 2 k 2 c 1 2 -1 c 3 2 -1 2 -1 m 2 e m -1 2 k b z 1 2 m -1 2 k c z c -1 -1 2 -1 b z 1 2 m -1 2 k -1 c z c -1 m SuperPlus [/itex]

 Rule Form

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

 2002-12-18