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/01.20.21.1396.01

 Input Form

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

 Standard Form

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RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]]]], ",", RowBox[List[RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "-", "p"]], ")"]], " ", SqrtBox["z"]]]]], "]"]]]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]], "\[And]", RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

 z n p z sin m ( b z ) cosh ( c z ) z - 2 - 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]]]]] ( Γ ( 2 ( n + 1 ) , ( - c - p ) z ) ( - c - p ) - 2 ( n + 1 ) + ( c - p ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( c - p ) z ) ) ( 1 - m mod 2 \$CellContext`m 2 ) - 2 - m 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]]]]] ( m π 2 Γ ( 2 ( n + 1 ) , ( - c + b ( m - 2 k ) - p ) z ) ( - c + b ( m - 2 k ) - p ) - 2 ( n + 1 ) + m π 2 ( c + b ( m - 2 k ) - p ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( c + b ( m - 2 k ) - p ) z ) + - 1 2 m π ( - c - b ( m - 2 k ) - p ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( - c - b ( m - 2 k ) - p ) z ) + - 1 2 m π ( c - b ( m - 2 k ) - p ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( c - b ( m - 2 k ) - p ) z ) ) /; m + n Condition z z n p z 1 2 b z 1 2 m c z 1 2 -1 2 -1 m Binomial m m 2 -1 Gamma 2 n 1 -1 c -1 p z 1 2 -1 c -1 p -2 n 1 c -1 p -2 n 1 Gamma 2 n 1 c -1 p z 1 2 1 -1 \$CellContext`m 2 -1 2 -1 m k 0 m -1 2 -1 -1 k Binomial m k m 2 -1 Gamma 2 n 1 -1 c b m -1 2 k -1 p z 1 2 -1 c b m -1 2 k -1 p -2 n 1 m 2 -1 c b m -1 2 k -1 p -2 n 1 Gamma 2 n 1 c b m -1 2 k -1 p z 1 2 -1 1 2 m -1 c -1 b m -1 2 k -1 p -2 n 1 Gamma 2 n 1 -1 c -1 b m -1 2 k -1 p z 1 2 -1 1 2 m c -1 b m -1 2 k -1 p -2 n 1 Gamma 2 n 1 c -1 b m -1 2 k -1 p z 1 2 m SuperPlus n [/itex]

 Rule Form

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

 2002-12-18