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/01.20.21.1044.01

 Input Form

 Integrate[z^n Cos[b z^2] Cosh[f z + g], z] == (1/8) ((-((-I) b)^(-1 - n)) E^(-((I f^2)/(4 b)) - g) Sum[2^(j - n) f^(-j + n) (-f - 2 I b z)^(1 + j) (-((I (-f - 2 I b z)^2)/b))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((I (-f - 2 I b z)^2)/(4 b))], {j, 0, n}] - ((-I) b)^(-1 - n) E^(-((I f^2)/(4 b)) + g) Sum[2^(j - n) (-f)^(-j + n) (f - 2 I b z)^(1 + j) (-((I (f - 2 I b z)^2)/b))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((I (f - 2 I b z)^2)/(4 b))], {j, 0, n}] - (I b)^(-1 - n) E^((I f^2)/(4 b) - g) Sum[2^(j - n) f^(-j + n) (-f + 2 I b z)^(1 + j) ((I (-f + 2 I b z)^2)/b)^ ((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, (I (-f + 2 I b z)^2)/(4 b)], {j, 0, n}] - (I b)^(-1 - n) E^((I f^2)/(4 b) + g) Sum[2^(j - n) (-f)^(-j + n) (f + 2 I b z)^(1 + j) ((I (f + 2 I b z)^2)/b)^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, (I (f + 2 I b z)^2)/(4 b)], {j, 0, n}]) /; Element[n, Integers] && n >= 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["z", "n"], RowBox[List["Cos", "[", RowBox[List["b", " ", SuperscriptBox["z", "2"]]], "]"]], RowBox[List["Cosh", "[", RowBox[List[RowBox[List["f", " ", "z"]], "+", "g"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["f", "2"]]], RowBox[List["4", " ", "b"]]]]], "-", "g"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox["f", RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "f"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "f"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], "2"]]], "b"]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "f"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], "2"]]], RowBox[List["4", " ", "b"]]]]]]], "]"]]]]]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["f", "2"]]], RowBox[List["4", " ", "b"]]]]], "+", "g"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "f"]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["f", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["f", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], "2"]]], "b"]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["f", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], "2"]]], RowBox[List["4", " ", "b"]]]]]]], "]"]]]]]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "b"]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["f", "2"]]], RowBox[List["4", " ", "b"]]], "-", "g"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox["f", RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "f"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "f"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], "2"]]], "b"], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "f"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], "2"]]], RowBox[List["4", " ", "b"]]]]], "]"]]]]]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "b"]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["f", "2"]]], RowBox[List["4", " ", "b"]]], "+", "g"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "f"]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["f", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["f", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], "2"]]], "b"], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["f", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], "2"]]], RowBox[List["4", " ", "b"]]]]], "]"]]]]]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

 z n cos ( b z 2 ) cosh ( g + f z ) z 1 8 ( - - f 2 4 b + g ( j = 0 n 2 j - n ( - f ) n - j ( f - 2 b z ) j + 1 ( - ( f - 2 b z ) 2 b ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( f - 2 b z ) 2 4 b ) ) ( - b ) - n - 1 - ( b ) - n - 1 f 2 4 b - g j = 0 n 2 j - n f n - j ( 2 b z - f ) j + 1 ( ( 2 b z - f ) 2 b ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , ( 2 b z - f ) 2 4 b ) - ( b ) - n - 1 f 2 4 b + g j = 0 n 2 j - n ( - f ) n - j ( f + 2 b z ) j + 1 ( ( f + 2 b z ) 2 b ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , ( f + 2 b z ) 2 4 b ) - ( - b ) - n - 1 - f 2 4 b - g j = 0 n 2 j - n f n - j ( - f - 2 b z ) j + 1 ( - ( - f - 2 b z ) 2 b ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( - f - 2 b z ) 2 4 b ) ) /; n Condition z z n b z 2 g f z 1 8 -1 -1 f 2 4 b -1 g j 0 n 2 j -1 n -1 f n -1 j f -1 2 b z j 1 -1 f -1 2 b z 2 b -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 f -1 2 b z 2 4 b -1 -1 b -1 n -1 -1 b -1 n -1 f 2 4 b -1 -1 g j 0 n 2 j -1 n f n -1 j 2 b z -1 f j 1 2 b z -1 f 2 b -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 2 b z -1 f 2 4 b -1 -1 b -1 n -1 f 2 4 b -1 g j 0 n 2 j -1 n -1 f n -1 j f 2 b z j 1 f 2 b z 2 b -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 f 2 b z 2 4 b -1 -1 -1 b -1 n -1 -1 f 2 4 b -1 -1 g j 0 n 2 j -1 n f n -1 j -1 f -1 2 b z j 1 -1 -1 f -1 2 b z 2 b -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 -1 f -1 2 b z 2 4 b -1 n [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", "n_"], " ", RowBox[List["Cos", "[", RowBox[List["b_", " ", SuperscriptBox["z_", "2"]]], "]"]], " ", RowBox[List["Cosh", "[", RowBox[List[RowBox[List["f_", " ", "z_"]], "+", "g_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["f", "2"]]], RowBox[List["4", " ", "b"]]]]], "-", "g"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox["f", RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "f"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "f"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], "2"]]], "b"]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "f"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], "2"]]], RowBox[List["4", " ", "b"]]]]]]], "]"]]]]]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["f", "2"]]], RowBox[List["4", " ", "b"]]]]], "+", "g"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "f"]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["f", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["f", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], "2"]]], "b"]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["f", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], "2"]]], RowBox[List["4", " ", "b"]]]]]]], "]"]]]]]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "b"]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["f", "2"]]], RowBox[List["4", " ", "b"]]], "-", "g"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox["f", RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "f"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "f"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], "2"]]], "b"], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "f"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], "2"]]], RowBox[List["4", " ", "b"]]]]], "]"]]]]]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "b"]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["f", "2"]]], RowBox[List["4", " ", "b"]]], "+", "g"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "f"]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["f", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["f", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], "2"]]], "b"], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["f", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], "2"]]], RowBox[List["4", " ", "b"]]]]], "]"]]]]]]]]]], ")"]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]

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

 2002-12-18