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/01.20.21.1392.01

 Input Form

 Integrate[z^n E^(p z) Sin[b z^2]^m Cosh[c z^2], z] == 2^(-2 - m) (((-c)^(-1 - n) Binomial[m, m/2] (-1 + Mod[m, 2]) (E^(p^2/(2 c)) Sum[2^(-n + q) (-p)^(n - q) (p - 2 c z)^(1 + q) ((p - 2 c z)^2/c)^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, (p - 2 c z)^2/(4 c)], {q, 0, n}] - (-1)^n Sum[2^(-n + q) (-p)^(n - q) (p + 2 c z)^(1 + q) (-((p + 2 c z)^2/c))^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((p + 2 c z)^2/(4 c))], {q, 0, n}]))/ E^(p^2/(4 c)) + (-I)^m Sum[(-1)^k Binomial[m, k] (-(E^(p^2/(4 c + 8 I b k - 4 I b m)) Sum[2^(-n + q) (-c - 2 I b k + I b m)^(-(1/2) - n) (-p)^(n - q) (p - 2 (c + 2 I b k - I b m) z)^(1 + q) ((p - 2 (c + 2 I b k - I b m) z)^2/(c + I b (2 k - m)))^ ((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, (p - 2 (c + 2 I b k - I b m) z)^2/(4 (c + I b (2 k - m)))], {q, 0, n}])/Sqrt[-c - 2 I b k + I b m] - (E^(p^2/(-4 c - 8 I b k + 4 I b m) + I m Pi) Sum[2^(-n + q) (c + 2 I b k - I b m)^(-(1/2) - n) (-p)^(n - q) (p + 2 (c + 2 I b k - I b m) z)^(1 + q) (-((p + 2 (c + 2 I b k - I b m) z)^2/(c + 2 I b k - I b m)))^ ((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((p + 2 (c + 2 I b k - I b m) z)^2/(4 (c + 2 I b k - I b m)))], {q, 0, n}])/Sqrt[c + 2 I b k - I b m] - (E^(p^2/(4 c - 8 I b k + 4 I b m) + I m Pi) Sum[2^(-n + q) (-c + 2 I b k - I b m)^(-(1/2) - n) (-p)^(n - q) (p - 2 (c - 2 I b k + I b m) z)^(1 + q) ((p - 2 (c - 2 I b k + I b m) z)^2/(c - 2 I b k + I b m))^ ((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, (p - 2 (c - 2 I b k + I b m) z)^2/(4 (c - 2 I b k + I b m))], {q, 0, n}])/Sqrt[-c + 2 I b k - I b m] - (E^(p^2/(-4 c + 8 I b k - 4 I b m)) Sum[2^(-n + q) (c - 2 I b k + I b m)^(-(1/2) - n) (-p)^(n - q) (p + 2 (c - 2 I b k + I b m) z)^(1 + q) (-((p + 2 (c - 2 I b k + I b m) z)^2/(c - 2 I b k + I b m)))^ ((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((p + 2 (c - 2 I b k + I b m) z)^2/(4 (c - 2 I b k + I b m)))], {q, 0, n}])/Sqrt[c - 2 I b k + I b m]), {k, 0, Floor[(1/2) (-1 + m)]}]) /; Element[m, Integers] && m > 0 && Element[n, Integers] && n >= 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["z", "n"], SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", "z"]]], " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["b", " ", SuperscriptBox["z", "2"]]], "]"]], "m"], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", SuperscriptBox["z", "2"]]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", "m"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "c"]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["p", "2"], RowBox[List["4", " ", "c"]]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["p", "2"], RowBox[List["2", " ", "c"]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "p"]], ")"]], RowBox[List["n", "-", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["p", "-", RowBox[List["2", " ", "c", " ", "z"]]]], ")"]], RowBox[List["1", "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["p", "-", RowBox[List["2", " ", "c", " ", "z"]]]], ")"]], "2"], "c"], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "q"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "q"]], "2"], ",", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["p", "-", RowBox[List["2", " ", "c", " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", "c"]]]]], "]"]]]]]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "p"]], ")"]], RowBox[List["n", "-", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["p", "+", RowBox[List["2", " ", "c", " ", "z"]]]], ")"]], RowBox[List["1", "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["p", "+", RowBox[List["2", " ", "c", " ", "z"]]]], ")"]], "2"], "c"]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "q"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "q"]], "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["p", "+", RowBox[List["2", " ", "c", " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", "c"]]]]]]], "]"]]]]]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "\[ImaginaryI]"]], ")"]], "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"]], ")"]]]], "]"]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", "k"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["p", "2"], RowBox[List[RowBox[List["4", " ", "c"]], "+", RowBox[List["8", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["4", " ", "\[ImaginaryI]", " ", "b", " ", "m"]]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "p"]], ")"]], RowBox[List["n", "-", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["p", "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["p", "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "q"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "q"]], "2"], ",", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["p", "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]]]], ")"]]]]]]], "]"]]]]]]]], ")"]]]], "/", RowBox[List["(", SqrtBox[RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]]], ")"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[SuperscriptBox["p", "2"], RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", "c"]], "-", RowBox[List["8", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["4", " ", "\[ImaginaryI]", " ", "b", " ", "m"]]]]], "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "p"]], ")"]], RowBox[List["n", "-", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["p", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["p", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["c", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "q"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "q"]], "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["p", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]]]]]]]]], "]"]]]]]]]], ")"]], "/", RowBox[List["(", SqrtBox[RowBox[List["c", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]]], ")"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[SuperscriptBox["p", "2"], RowBox[List[RowBox[List["4", " ", "c"]], "-", RowBox[List["8", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["4", " ", "\[ImaginaryI]", " ", "b", " ", "m"]]]]], "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "p"]], ")"]], RowBox[List["n", "-", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["p", "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["p", "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["c", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "q"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "q"]], "2"], ",", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["p", "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]]]]]]], "]"]]]]]]]], ")"]], "/", RowBox[List["(", SqrtBox[RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]]], ")"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["p", "2"], RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", "c"]], "+", RowBox[List["8", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["4", " ", "\[ImaginaryI]", " ", "b", " ", "m"]]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "p"]], ")"]], RowBox[List["n", "-", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["p", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["p", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["c", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "q"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "q"]], "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["p", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]]]]]]]]], "]"]]]]]]]], ")"]], "/", RowBox[List["(", SqrtBox[RowBox[List["c", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]]], ")"]]]]]], ")"]]]]]]]]]], ")"]]]]]], "/;", 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 2 ) cosh ( c z 2 ) z 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]]]]] ( - 1 - c - 2 b k + b m ( p 2 4 c + 8 b k - 4 b m q = 0 n 2 q - n ( - c - 2 b k + b m ) - n - 1 2 ( - p ) n - q ( p - 2 ( c + 2 b k - b m ) z ) q + 1 ( ( p - 2 ( c + 2 b k - b m ) z ) 2 c + b ( 2 k - m ) ) 1 2 ( - q - 1 ) ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , ( p - 2 ( c + 2 b k - b m ) z ) 2 4 ( c + b ( 2 k - m ) ) ) ) - 1 c - 2 b k + b m ( p 2 - 4 c + 8 b k - 4 b m q = 0 n 2 q - n ( c - 2 b k + b m ) - n - 1 2 ( - p ) n - q ( p + 2 ( c - 2 b k + b m ) z ) q + 1 ( - ( p + 2 ( c - 2 b k + b m ) z ) 2 c - 2 b k + b m ) 1 2 ( - q - 1 ) ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , - ( p + 2 ( c - 2 b k + b m ) z ) 2 4 ( c - 2 b k + b m ) ) ) - 1 - c + 2 b k - b m ( p 2 4 c - 8 b k + 4 b m + m π q = 0 n 2 q - n ( - c + 2 b k - b m ) - n - 1 2 ( - p ) n - q ( p - 2 ( c - 2 b k + b m ) z ) q + 1 ( ( p - 2 ( c - 2 b k + b m ) z ) 2 c - 2 b k + b m ) 1 2 ( - q - 1 ) ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , ( p - 2 ( c - 2 b k + b m ) z ) 2 4 ( c - 2 b k + b m ) ) ) - 1 c + 2 b k - b m ( p 2 - 4 c - 8 b k + 4 b m + m π q = 0 n 2 q - n ( c + 2 b k - b m ) - n - 1 2 ( - p ) n - q ( p + 2 ( c + 2 b k - b m ) z ) q + 1 ( - ( p + 2 ( c + 2 b k - b m ) z ) 2 c + 2 b k - b m ) 1 2 ( - q - 1 ) ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , - ( p + 2 ( c + 2 b k - b m ) z ) 2 4 ( c + 2 b k - b m ) ) ) ) ) ( - ) m + ( - c ) - n - 1 - p 2 4 c ( 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]]]]] ( m mod 2 \$CellContext`m 2 - 1 ) ( p 2 2 c q = 0 n 2 q - n ( - p ) n - q ( p - 2 c z ) q + 1 ( ( p - 2 c z ) 2 c ) 1 2 ( - q - 1 ) ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , ( p - 2 c z ) 2 4 c ) - ( - 1 ) n q = 0 n 2 q - n ( - p ) n - q ( p + 2 c z ) q + 1 ( - ( p + 2 c z ) 2 c ) 1 2 ( - q - 1 ) ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , - ( p + 2 c z ) 2 4 c ) ) ) /; m + n Condition z z n p z b z 2 m c z 2 2 -1 m -2 k 0 m -1 2 -1 -1 k Binomial m k -1 1 -1 c -1 2 b k b m 1 2 -1 p 2 4 c 8 b k -1 4 b m -1 q 0 n 2 q -1 n -1 c -1 2 b k b m -1 n -1 1 2 -1 p n -1 q p -1 2 c 2 b k -1 b m z q 1 p -1 2 c 2 b k -1 b m z 2 c b 2 k -1 m -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 p -1 2 c 2 b k -1 b m z 2 4 c b 2 k -1 m -1 -1 1 c -1 2 b k b m 1 2 -1 p 2 -4 c 8 b k -1 4 b m -1 q 0 n 2 q -1 n c -1 2 b k b m -1 n -1 1 2 -1 p n -1 q p 2 c -1 2 b k b m z q 1 -1 p 2 c -1 2 b k b m z 2 c -1 2 b k b m -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 -1 p 2 c -1 2 b k b m z 2 4 c -1 2 b k b m -1 -1 1 -1 c 2 b k -1 b m 1 2 -1 p 2 4 c -1 8 b k 4 b m -1 m q 0 n 2 q -1 n -1 c 2 b k -1 b m -1 n -1 1 2 -1 p n -1 q p -1 2 c -1 2 b k b m z q 1 p -1 2 c -1 2 b k b m z 2 c -1 2 b k b m -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 p -1 2 c -1 2 b k b m z 2 4 c -1 2 b k b m -1 -1 1 c 2 b k -1 b m 1 2 -1 p 2 -4 c -1 8 b k 4 b m -1 m q 0 n 2 q -1 n c 2 b k -1 b m -1 n -1 1 2 -1 p n -1 q p 2 c 2 b k -1 b m z q 1 -1 p 2 c 2 b k -1 b m z 2 c 2 b k -1 b m -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 -1 p 2 c 2 b k -1 b m z 2 4 c 2 b k -1 b m -1 -1 m -1 c -1 n -1 -1 p 2 4 c -1 Binomial m m 2 -1 \$CellContext`m 2 -1 p 2 2 c -1 q 0 n 2 q -1 n -1 p n -1 q p -1 2 c z q 1 p -1 2 c z 2 c -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 p -1 2 c z 2 4 c -1 -1 -1 n q 0 n 2 q -1 n -1 p n -1 q p 2 c z q 1 -1 p 2 c z 2 c -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 -1 p 2 c z 2 4 c -1 m SuperPlus n [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", "n_"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["p_", " ", "z_"]]], " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["b_", " ", SuperscriptBox["z_", "2"]]], "]"]], "m_"], " ", RowBox[List["Cosh", "[", RowBox[List["c_", " ", SuperscriptBox["z_", "2"]]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", "m"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "c"]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["p", "2"], RowBox[List["4", " ", "c"]]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["p", "2"], RowBox[List["2", " ", "c"]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "p"]], ")"]], RowBox[List["n", "-", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["p", "-", RowBox[List["2", " ", "c", " ", "z"]]]], ")"]], RowBox[List["1", "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["p", "-", RowBox[List["2", " ", "c", " ", "z"]]]], ")"]], "2"], "c"], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "q"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "q"]], "2"], ",", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["p", "-", RowBox[List["2", " ", "c", " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", "c"]]]]], "]"]]]]]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "p"]], ")"]], RowBox[List["n", "-", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["p", "+", RowBox[List["2", " ", "c", " ", "z"]]]], ")"]], RowBox[List["1", "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["p", "+", RowBox[List["2", " ", "c", " ", "z"]]]], ")"]], "2"], "c"]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "q"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "q"]], "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["p", "+", RowBox[List["2", " ", "c", " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", "c"]]]]]]], "]"]]]]]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "\[ImaginaryI]"]], ")"]], "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"]], ")"]]]], "]"]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", "k"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["p", "2"], RowBox[List[RowBox[List["4", " ", "c"]], "+", RowBox[List["8", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["4", " ", "\[ImaginaryI]", " ", "b", " ", "m"]]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "p"]], ")"]], RowBox[List["n", "-", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["p", "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["p", "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "q"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "q"]], "2"], ",", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["p", "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]]]], ")"]]]]]]], "]"]]]]]]]], SqrtBox[RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]]]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[SuperscriptBox["p", "2"], RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", "c"]], "-", RowBox[List["8", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["4", " ", "\[ImaginaryI]", " ", "b", " ", "m"]]]]], "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "p"]], ")"]], RowBox[List["n", "-", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["p", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["p", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["c", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "q"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "q"]], "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["p", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]]]]]]]]], "]"]]]]]]]], SqrtBox[RowBox[List["c", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[SuperscriptBox["p", "2"], RowBox[List[RowBox[List["4", " ", "c"]], "-", RowBox[List["8", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["4", " ", "\[ImaginaryI]", " ", "b", " ", "m"]]]]], "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "p"]], ")"]], RowBox[List["n", "-", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["p", "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["p", "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["c", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "q"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "q"]], "2"], ",", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["p", "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]]]]]]], "]"]]]]]]]], SqrtBox[RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["p", "2"], RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", "c"]], "+", RowBox[List["8", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["4", " ", "\[ImaginaryI]", " ", "b", " ", "m"]]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "p"]], ")"]], RowBox[List["n", "-", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["p", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["p", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["c", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "q"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "q"]], "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["p", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]]]]]]]]], "]"]]]]]]]], SqrtBox[RowBox[List["c", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]]]]]], ")"]]]]]]]]]], ")"]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "&&", RowBox[List["m", ">", "0"]], "&&", RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]

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

 2002-12-18