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/01.20.21.3925.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

 2002-12-18