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/01.20.21.4916.01

 Input Form

 Integrate[z^n Sin[a Sqrt[z] + p z + q] Sinh[w Sqrt[z] + s z + t] Cosh[c Sqrt[z] + f z + g]^v, z] == I 2^(-3 - 2 n - v) Binomial[v, v/2] (1 - Mod[v, 2]) ((-E^((-I) q - t - ((-I) a - w)^2/(4 ((-I) p - s)))) ((-I) p - s)^(-2 - 2 n) Sum[(-1)^(i - l) 4^i ((-I) a - w)^ (-i - l + 2 n) ((-I) a - w + 2 ((-I) p - s) Sqrt[z])^(i + l) (-(((-I) a - w + 2 ((-I) p - s) Sqrt[z])^2/((-I) p - s)))^ ((1/2) (-1 - i - l)) Binomial[i, l] Binomial[n, i] (((-I) a - w) ((-I) a - w + 2 ((-I) p - s) Sqrt[z]) Gamma[(1/2) (1 + i + l), -(((-I) a - w + 2 ((-I) p - s) Sqrt[z])^2/ (4 ((-I) p - s)))] + 2 ((-I) p - s) Sqrt[-(((-I) a - w + 2 ((-I) p - s) Sqrt[z])^2/((-I) p - s))] Gamma[(1/2) (2 + i + l), -(((-I) a - w + 2 ((-I) p - s) Sqrt[z])^2/ (4 ((-I) p - s)))]), {i, 0, n}, {l, 0, i}] + E^(I q - t - (I a - w)^2/(4 (I p - s))) (I p - s)^(-2 - 2 n) Sum[(-1)^(i - l) 4^i (I a - w)^(-i - l + 2 n) (I a - w + 2 (I p - s) Sqrt[z])^(i + l) (-((I a - w + 2 (I p - s) Sqrt[z])^2/(I p - s)))^((1/2) (-1 - i - l)) Binomial[i, l] Binomial[n, i] ((I a - w) (I a - w + 2 (I p - s) Sqrt[z]) Gamma[(1/2) (1 + i + l), -((I a - w + 2 (I p - s) Sqrt[z])^2/(4 (I p - s)))] + 2 (I p - s) Sqrt[-((I a - w + 2 (I p - s) Sqrt[z])^2/(I p - s))] Gamma[(1/2) (2 + i + l), -((I a - w + 2 (I p - s) Sqrt[z])^2/ (4 (I p - s)))]), {i, 0, n}, {l, 0, i}] + E^((-I) q + t - ((-I) a + w)^2/(4 ((-I) p + s))) ((-I) p + s)^(-2 - 2 n) Sum[(-1)^(i - l) 4^i ((-I) a + w)^(-i - l + 2 n) ((-I) a + w + 2 ((-I) p + s) Sqrt[z])^(i + l) (-(((-I) a + w + 2 ((-I) p + s) Sqrt[z])^2/((-I) p + s)))^ ((1/2) (-1 - i - l)) Binomial[i, l] Binomial[n, i] (((-I) a + w) ((-I) a + w + 2 ((-I) p + s) Sqrt[z]) Gamma[(1/2) (1 + i + l), -(((-I) a + w + 2 ((-I) p + s) Sqrt[z])^2/ (4 ((-I) p + s)))] + 2 ((-I) p + s) Sqrt[-(((-I) a + w + 2 ((-I) p + s) Sqrt[z])^2/((-I) p + s))] Gamma[(1/2) (2 + i + l), -(((-I) a + w + 2 ((-I) p + s) Sqrt[z])^2/ (4 ((-I) p + s)))]), {i, 0, n}, {l, 0, i}] - E^(I q + t - (I a + w)^2/(4 (I p + s))) (I p + s)^(-2 - 2 n) Sum[(-1)^(i - l) 4^i (I a + w)^(-i - l + 2 n) (I a + w + 2 (I p + s) Sqrt[z])^(i + l) (-((I a + w + 2 (I p + s) Sqrt[z])^2/(I p + s)))^((1/2) (-1 - i - l)) Binomial[i, l] Binomial[n, i] ((I a + w) (I a + w + 2 (I p + s) Sqrt[z]) Gamma[(1/2) (1 + i + l), -((I a + w + 2 (I p + s) Sqrt[z])^2/(4 (I p + s)))] + 2 (I p + s) Sqrt[-((I a + w + 2 (I p + s) Sqrt[z])^2/(I p + s))] Gamma[(1/2) (2 + i + l), -((I a + w + 2 (I p + s) Sqrt[z])^2/ (4 (I p + s)))]), {i, 0, n}, {l, 0, i}]) + I 2^(-3 - 2 n - v) Sum[Binomial[v, h] ((-E^((-I) q - t + g (2 h - v) - ((-I) a + c (2 h - v) - w)^2/ (4 ((-I) p - s + f (2 h - v))))) ((-I) p - s + f (2 h - v))^ (-2 - 2 n) Sum[(-1)^(i - l) 4^i ((-I) a + c (2 h - v) - w)^ (-i - l + 2 n) ((-I) a + c (2 h - v) - w + 2 ((-I) p - s + f (2 h - v)) Sqrt[z])^(i + l) (-(((-I) a + c (2 h - v) - w + 2 ((-I) p - s + f (2 h - v)) Sqrt[z])^2/((-I) p - s + f (2 h - v))))^((1/2) (-1 - i - l)) Binomial[i, l] Binomial[n, i] (((-I) a + c (2 h - v) - w) ((-I) a + c (2 h - v) - w + 2 ((-I) p - s + f (2 h - v)) Sqrt[z]) Gamma[(1/2) (1 + i + l), -(((-I) a + c (2 h - v) - w + 2 ((-I) p - s + f (2 h - v)) Sqrt[z])^2/(4 ((-I) p - s + f (2 h - v))))] + 2 ((-I) p - s + f (2 h - v)) Sqrt[-(((-I) a + c (2 h - v) - w + 2 ((-I) p - s + f (2 h - v)) Sqrt[z])^2/((-I) p - s + f (2 h - v)))] Gamma[(1/2) (2 + i + l), -(((-I) a + c (2 h - v) - w + 2 ((-I) p - s + f (2 h - v)) Sqrt[z])^2/(4 ((-I) p - s + f (2 h - v))))]), {i, 0, n}, {l, 0, i}] + E^(I q - t + g (2 h - v) - (I a + c (2 h - v) - w)^2/ (4 (I p - s + f (2 h - v)))) (I p - s + f (2 h - v))^(-2 - 2 n) Sum[(-1)^(i - l) 4^i (I a + c (2 h - v) - w)^(-i - l + 2 n) (I a + c (2 h - v) - w + 2 (I p - s + f (2 h - v)) Sqrt[z])^(i + l) (-((I a + c (2 h - v) - w + 2 (I p - s + f (2 h - v)) Sqrt[z])^2/ (I p - s + f (2 h - v))))^((1/2) (-1 - i - l)) Binomial[i, l] Binomial[n, i] ((I a + c (2 h - v) - w) (I a + c (2 h - v) - w + 2 (I p - s + f (2 h - v)) Sqrt[z]) Gamma[(1/2) (1 + i + l), -((I a + c (2 h - v) - w + 2 (I p - s + f (2 h - v)) Sqrt[z])^2/( 4 (I p - s + f (2 h - v))))] + 2 (I p - s + f (2 h - v)) Sqrt[-((I a + c (2 h - v) - w + 2 (I p - s + f (2 h - v)) Sqrt[z])^2/(I p - s + f (2 h - v)))] Gamma[(1/2) (2 + i + l), -((I a + c (2 h - v) - w + 2 (I p - s + f (2 h - v)) Sqrt[z])^2/(4 (I p - s + f (2 h - v))))]), {i, 0, n}, {l, 0, i}] + E^((-I) q + t + g (2 h - v) - ((-I) a + c (2 h - v) + w)^2/ (4 ((-I) p + s + f (2 h - v)))) ((-I) p + s + f (2 h - v))^ (-2 - 2 n) Sum[(-1)^(i - l) 4^i ((-I) a + c (2 h - v) + w)^ (-i - l + 2 n) ((-I) a + c (2 h - v) + w + 2 ((-I) p + s + f (2 h - v)) Sqrt[z])^(i + l) (-(((-I) a + c (2 h - v) + w + 2 ((-I) p + s + f (2 h - v)) Sqrt[z])^2/((-I) p + s + f (2 h - v))))^((1/2) (-1 - i - l)) Binomial[i, l] Binomial[n, i] (((-I) a + c (2 h - v) + w) ((-I) a + c (2 h - v) + w + 2 ((-I) p + s + f (2 h - v)) Sqrt[z]) Gamma[(1/2) (1 + i + l), -(((-I) a + c (2 h - v) + w + 2 ((-I) p + s + f (2 h - v)) Sqrt[z])^2/(4 ((-I) p + s + f (2 h - v))))] + 2 ((-I) p + s + f (2 h - v)) Sqrt[-(((-I) a + c (2 h - v) + w + 2 ((-I) p + s + f (2 h - v)) Sqrt[z])^2/((-I) p + s + f (2 h - v)))] Gamma[(1/2) (2 + i + l), -(((-I) a + c (2 h - v) + w + 2 ((-I) p + s + f (2 h - v)) Sqrt[z])^2/(4 ((-I) p + s + f (2 h - v))))]), {i, 0, n}, {l, 0, i}] - E^(I q + t + g (2 h - v) - (I a + c (2 h - v) + w)^2/ (4 (I p + s + f (2 h - v)))) (I p + s + f (2 h - v))^(-2 - 2 n) Sum[(-1)^(i - l) 4^i (I a + c (2 h - v) + w)^(-i - l + 2 n) (I a + c (2 h - v) + w + 2 (I p + s + f (2 h - v)) Sqrt[z])^(i + l) (-((I a + c (2 h - v) + w + 2 (I p + s + f (2 h - v)) Sqrt[z])^2/ (I p + s + f (2 h - v))))^((1/2) (-1 - i - l)) Binomial[i, l] Binomial[n, i] ((I a + c (2 h - v) + w) (I a + c (2 h - v) + w + 2 (I p + s + f (2 h - v)) Sqrt[z]) Gamma[(1/2) (1 + i + l), -((I a + c (2 h - v) + w + 2 (I p + s + f (2 h - v)) Sqrt[z])^2/( 4 (I p + s + f (2 h - v))))] + 2 (I p + s + f (2 h - v)) Sqrt[-((I a + c (2 h - v) + w + 2 (I p + s + f (2 h - v)) Sqrt[z])^2/(I p + s + f (2 h - v)))] Gamma[(1/2) (2 + i + l), -((I a + c (2 h - v) + w + 2 (I p + s + f (2 h - v)) Sqrt[z])^2/(4 (I p + s + f (2 h - v))))]), {i, 0, n}, {l, 0, i}] - E^((-I) q - t + g (-2 h + v) - ((-I) a + c (-2 h + v) - w)^2/ (4 ((-I) p - s + f (-2 h + v)))) ((-I) p - s + f (-2 h + v))^ (-2 - 2 n) Sum[(-1)^(i - l) 4^i ((-I) a + c (-2 h + v) - w)^ (-i - l + 2 n) ((-I) a + c (-2 h + v) - w + 2 ((-I) p - s + f (-2 h + v)) Sqrt[z])^(i + l) (-(((-I) a + c (-2 h + v) - w + 2 ((-I) p - s + f (-2 h + v)) Sqrt[z])^2/((-I) p - s + f (-2 h + v))))^((1/2) (-1 - i - l)) Binomial[i, l] Binomial[n, i] (((-I) a + c (-2 h + v) - w) ((-I) a + c (-2 h + v) - w + 2 ((-I) p - s + f (-2 h + v)) Sqrt[z]) Gamma[(1/2) (1 + i + l), -(((-I) a + c (-2 h + v) - w + 2 ((-I) p - s + f (-2 h + v)) Sqrt[z])^2/(4 ((-I) p - s + f (-2 h + v))))] + 2 ((-I) p - s + f (-2 h + v)) Sqrt[-(((-I) a + c (-2 h + v) - w + 2 ((-I) p - s + f (-2 h + v)) Sqrt[z])^2/((-I) p - s + f (-2 h + v)))] Gamma[(1/2) (2 + i + l), -(((-I) a + c (-2 h + v) - w + 2 ((-I) p - s + f (-2 h + v)) Sqrt[z])^2/(4 ((-I) p - s + f (-2 h + v))))]), {i, 0, n}, {l, 0, i}] + E^(I q - t + g (-2 h + v) - (I a + c (-2 h + v) - w)^2/ (4 (I p - s + f (-2 h + v)))) (I p - s + f (-2 h + v))^(-2 - 2 n) Sum[(-1)^(i - l) 4^i (I a + c (-2 h + v) - w)^(-i - l + 2 n) (I a + c (-2 h + v) - w + 2 (I p - s + f (-2 h + v)) Sqrt[z])^ (i + l) (-((I a + c (-2 h + v) - w + 2 (I p - s + f (-2 h + v)) Sqrt[z])^2/(I p - s + f (-2 h + v))))^((1/2) (-1 - i - l)) Binomial[i, l] Binomial[n, i] ((I a + c (-2 h + v) - w) (I a + c (-2 h + v) - w + 2 (I p - s + f (-2 h + v)) Sqrt[z]) Gamma[(1/2) (1 + i + l), -((I a + c (-2 h + v) - w + 2 (I p - s + f (-2 h + v)) Sqrt[z])^2/(4 (I p - s + f (-2 h + v))))] + 2 (I p - s + f (-2 h + v)) Sqrt[-((I a + c (-2 h + v) - w + 2 (I p - s + f (-2 h + v)) Sqrt[z])^2/(I p - s + f (-2 h + v)))] Gamma[(1/2) (2 + i + l), -((I a + c (-2 h + v) - w + 2 (I p - s + f (-2 h + v)) Sqrt[z])^2/(4 (I p - s + f (-2 h + v))))]), {i, 0, n}, {l, 0, i}] + E^((-I) q + t + g (-2 h + v) - ((-I) a + c (-2 h + v) + w)^2/ (4 ((-I) p + s + f (-2 h + v)))) ((-I) p + s + f (-2 h + v))^ (-2 - 2 n) Sum[(-1)^(i - l) 4^i ((-I) a + c (-2 h + v) + w)^ (-i - l + 2 n) ((-I) a + c (-2 h + v) + w + 2 ((-I) p + s + f (-2 h + v)) Sqrt[z])^(i + l) (-(((-I) a + c (-2 h + v) + w + 2 ((-I) p + s + f (-2 h + v)) Sqrt[z])^2/((-I) p + s + f (-2 h + v))))^((1/2) (-1 - i - l)) Binomial[i, l] Binomial[n, i] (((-I) a + c (-2 h + v) + w) ((-I) a + c (-2 h + v) + w + 2 ((-I) p + s + f (-2 h + v)) Sqrt[z]) Gamma[(1/2) (1 + i + l), -(((-I) a + c (-2 h + v) + w + 2 ((-I) p + s + f (-2 h + v)) Sqrt[z])^2/(4 ((-I) p + s + f (-2 h + v))))] + 2 ((-I) p + s + f (-2 h + v)) Sqrt[-(((-I) a + c (-2 h + v) + w + 2 ((-I) p + s + f (-2 h + v)) Sqrt[z])^2/((-I) p + s + f (-2 h + v)))] Gamma[(1/2) (2 + i + l), -(((-I) a + c (-2 h + v) + w + 2 ((-I) p + s + f (-2 h + v)) Sqrt[z])^2/(4 ((-I) p + s + f (-2 h + v))))]), {i, 0, n}, {l, 0, i}] - E^(I q + t + g (-2 h + v) - (I a + c (-2 h + v) + w)^2/ (4 (I p + s + f (-2 h + v)))) (I p + s + f (-2 h + v))^(-2 - 2 n) Sum[(-1)^(i - l) 4^i (I a + c (-2 h + v) + w)^(-i - l + 2 n) (I a + c (-2 h + v) + w + 2 (I p + s + f (-2 h + v)) Sqrt[z])^ (i + l) (-((I a + c (-2 h + v) + w + 2 (I p + s + f (-2 h + v)) Sqrt[z])^2/(I p + s + f (-2 h + v))))^((1/2) (-1 - i - l)) Binomial[i, l] Binomial[n, i] ((I a + c (-2 h + v) + w) (I a + c (-2 h + v) + w + 2 (I p + s + f (-2 h + v)) Sqrt[z]) Gamma[(1/2) (1 + i + l), -((I a + c (-2 h + v) + w + 2 (I p + s + f (-2 h + v)) Sqrt[z])^2/(4 (I p + s + f (-2 h + v))))] + 2 (I p + s + f (-2 h + v)) Sqrt[-((I a + c (-2 h + v) + w + 2 (I p + s + f (-2 h + v)) Sqrt[z])^2/(I p + s + f (-2 h + v)))] Gamma[(1/2) (2 + i + l), -((I a + c (-2 h + v) + w + 2 (I p + s + f (-2 h + v)) Sqrt[z])^2/(4 (I p + s + f (-2 h + v))))]), {i, 0, n}, {l, 0, i}]), {h, 0, Floor[(1/2) (-1 + v)]}] /; Element[n, Integers] && n >= 0 && Element[v, Integers] && v > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["z", "n"], RowBox[List["Sin", "[", RowBox[List[RowBox[List["a", " ", SqrtBox["z"]]], "+", RowBox[List["p", " ", "z"]], "+", "q"]], "]"]], RowBox[List["Sinh", "[", RowBox[List[RowBox[List["w", " ", SqrtBox["z"]]], "+", RowBox[List["s", " ", "z"]], "+", "t"]], "]"]], SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List["f", " ", "z"]], "+", "g"]], "]"]], "v"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "3"]], "-", RowBox[List["2", " ", "n"]], "-", "v"]]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", 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"p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], "/", RowBox[List["(", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]]]], ")"]]]], ")"]]]]]]]], "]"]]]]]], ")"]]]]]]]]]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]], "\[And]", RowBox[List["v", "\[Element]", "Integers"]], "\[And]", RowBox[List["v", ">", "0"]]]]]]]]

 MathML Form

 z n sin ( z a + q + p z ) sinh ( t + s z + w z ) cosh v ( z c + g + f z ) z 2 - 2 n - v - 3 ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity, Rule[Editable, True]]], List[TagBox[FractionBox["v", "2"], Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( 1 - v mod 2 \$CellContext`v 2 ) ( - - ( - a - w ) 2 4 ( - p - s ) - q - t ( i = 0 n l = 0 i ( - 1 ) i - l 4 i ( - a - w ) - i - l + 2 n ( - a - w + 2 ( - p - s ) z ) i + l ( - ( - a - w + 2 ( - p - s ) z ) 2 - p - s ) 1 2 ( - i - l - 1 ) ( i l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity, Rule[Editable, True]]], List[TagBox["l", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["i", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( ( - a - w ) ( - a - w + 2 ( - p - s ) z ) Γ ( 1 2 ( i + l + 1 ) , - ( - a - w + 2 ( - p - s ) z ) 2 4 ( - p - s ) ) + 2 - ( - a - w + 2 ( - p - s ) z ) 2 - p - s ( - p - s ) Γ ( 1 2 ( i + l + 2 ) , - ( - a - w + 2 ( - p - s ) z ) 2 4 ( - p - s ) ) ) ) ( - p - s ) - 2 n - 2 + - ( a - w ) 2 4 ( p - s ) + q - t ( p - s ) - 2 n - 2 i = 0 n l = 0 i ( - 1 ) i - l 4 i ( a - w ) - i - l + 2 n ( a - w + 2 ( p - s ) z ) i + l ( - ( a - w + 2 ( p - s ) z ) 2 p - s ) 1 2 ( - i - l - 1 ) ( i l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity, Rule[Editable, True]]], List[TagBox["l", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["i", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( ( a - w ) ( a - w + 2 ( p - s ) z ) Γ ( 1 2 ( i + l + 1 ) , - ( a - w + 2 ( p - s ) z ) 2 4 ( p - s ) ) + 2 - ( a - w + 2 ( p - s ) z ) 2 p - s ( p - s ) Γ ( 1 2 ( i + l + 2 ) , - ( a - w + 2 ( p - s ) z ) 2 4 ( p - s ) ) ) + - ( - a + w ) 2 4 ( s - p ) - q + t ( s - p ) - 2 n - 2 i = 0 n l = 0 i ( - 1 ) i - l 4 i ( - a + w ) - i - l + 2 n ( - a + w + 2 ( s - p ) z ) i + l ( - ( - a + w + 2 ( s - p ) z ) 2 s - p ) 1 2 ( - i - l - 1 ) ( i l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity, Rule[Editable, True]]], List[TagBox["l", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["i", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( ( - a + w ) ( - a + w + 2 ( s - p ) z ) Γ ( 1 2 ( i + l + 1 ) , - ( - a + w + 2 ( s - p ) z ) 2 4 ( s - p ) ) + 2 - ( - a + w + 2 ( s - p ) z ) 2 s - p ( s - p ) Γ ( 1 2 ( i + l + 2 ) , - ( - a + w + 2 ( s - p ) z ) 2 4 ( s - p ) ) ) - - ( a + w ) 2 4 ( p + s ) + q + t ( p + s ) - 2 n - 2 i = 0 n l = 0 i ( - 1 ) i - l 4 i ( a + w ) - i - l + 2 n ( a + w + 2 ( p + s ) z ) i + l ( - ( a + w + 2 ( p + s ) z ) 2 p + s ) 1 2 ( - i - l - 1 ) ( i l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity, Rule[Editable, True]]], List[TagBox["l", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["i", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( ( a + w ) ( a + w + 2 ( p + s ) z ) Γ ( 1 2 ( i + l + 1 ) , - ( a + w + 2 ( p + s ) z ) 2 4 ( p + s ) ) + 2 - ( a + w + 2 ( p + s ) z ) 2 p + s ( p + s ) Γ ( 1 2 ( i + l + 2 ) , - ( a + w + 2 ( p + s ) z ) 2 4 ( p + s ) ) ) ) + 2 - 2 n - v - 3 h = 0 v - 1 2 ( v h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity, Rule[Editable, True]]], List[TagBox["h", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( - - ( - a + c ( 2 h - v ) - w ) 2 4 ( - p - s + f ( 2 h - v ) ) - q - t + g ( 2 h - v ) ( i = 0 n l = 0 i ( - 1 ) i - l 4 i ( - a + c ( 2 h - v ) - w ) - i - l + 2 n ( - a + c ( 2 h - v ) - w + 2 ( - p - s + f ( 2 h - v ) ) z ) i + l ( - ( - a + c ( 2 h - v ) - w + 2 ( - p - s + f ( 2 h - v ) ) z ) 2 - p - s + f ( 2 h - v ) ) 1 2 ( - i - l - 1 ) ( i l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity, Rule[Editable, True]]], List[TagBox["l", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["i", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( ( - a + c ( 2 h - v ) - w ) ( - a + c ( 2 h - v ) - w + 2 ( - p - s + f ( 2 h - v ) ) z ) Γ ( 1 2 ( i + l + 1 ) , - ( - a + c ( 2 h - v ) - w + 2 ( - p - s + f ( 2 h - v ) ) z ) 2 4 ( - p - s + f ( 2 h - v ) ) ) + 2 ( - p - s + f ( 2 h - v ) ) Γ ( 1 2 ( i + l + 2 ) , - ( - a + c ( 2 h - v ) - w + 2 ( - p - s + f ( 2 h - v ) ) z ) 2 4 ( - p - s + f ( 2 h - v ) ) ) - ( - a + c ( 2 h - v ) - w + 2 ( - p - s + f ( 2 h - v ) ) z ) 2 - p - s + f ( 2 h - v ) ) ) ( - p - s + f ( 2 h - v ) ) - 2 n - 2 + - ( a + c ( 2 h - v ) - w ) 2 4 ( p - s + f ( 2 h - v ) ) + q - t + g ( 2 h - v ) ( p - s + f ( 2 h - v ) ) - 2 n - 2 i = 0 n l = 0 i ( - 1 ) i - l 4 i ( a + c ( 2 h - v ) - w ) - i - l + 2 n ( a + c ( 2 h - v ) - w + 2 ( p - s + f ( 2 h - v ) ) z ) i + l ( - ( a + c ( 2 h - v ) - w + 2 ( p - s + f ( 2 h - v ) ) z ) 2 p - s + f ( 2 h - v ) ) 1 2 ( - i - l - 1 ) ( i l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity, Rule[Editable, True]]], List[TagBox["l", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["i", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( ( a + c ( 2 h - v ) - w ) ( a + c ( 2 h - v ) - w + 2 ( p - s + f ( 2 h - v ) ) z ) Γ ( 1 2 ( i + l + 1 ) , - ( a + c ( 2 h - v ) - w + 2 ( p - s + f ( 2 h - v ) ) z ) 2 4 ( p - s + f ( 2 h - v ) ) ) + 2 ( p - s + f ( 2 h - v ) ) Γ ( 1 2 ( i + l + 2 ) , - ( a + c ( 2 h - v ) - w + 2 ( p - s + f ( 2 h - v ) ) z ) 2 4 ( p - s + f ( 2 h - v ) ) ) - ( a + c ( 2 h - v ) - w + 2 ( p - s + f ( 2 h - v ) ) z ) 2 p - s + f ( 2 h - v ) ) + - ( - a + c ( 2 h - v ) + w ) 2 4 ( - p + s + f ( 2 h - v ) ) - q + t + g ( 2 h - v ) ( - p + s + f ( 2 h - v ) ) - 2 n - 2 i = 0 n l = 0 i ( - 1 ) i - l 4 i ( - a + c ( 2 h - v ) + w ) - i - l + 2 n ( - a + c ( 2 h - v ) + w + 2 ( - p + s + f ( 2 h - v ) ) z ) i + l ( - ( - a + c ( 2 h - v ) + w + 2 ( - p + s + f ( 2 h - v ) ) z ) 2 - p + s + f ( 2 h - v ) ) 1 2 ( - i - l - 1 ) ( i l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity, Rule[Editable, True]]], List[TagBox["l", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["i", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( ( - a + c ( 2 h - v ) + w ) ( - a + c ( 2 h - v ) + w + 2 ( - p + s + f ( 2 h - v ) ) z ) Γ ( 1 2 ( i + l + 1 ) , - ( - a + c ( 2 h - v ) + w + 2 ( - p + s + f ( 2 h - v ) ) z ) 2 4 ( - p + s + f ( 2 h - v ) ) ) + 2 ( - p + s + f ( 2 h - v ) ) Γ ( 1 2 ( i + l + 2 ) , - ( - a + c ( 2 h - v ) + w + 2 ( - p + s + f ( 2 h - v ) ) z ) 2 4 ( - p + s + f ( 2 h - v ) ) ) - ( - a + c ( 2 h - v ) + w + 2 ( - p + s + f ( 2 h - v ) ) z ) 2 - p + s + f ( 2 h - v ) ) - - ( a + c ( 2 h - v ) + w ) 2 4 ( p + s + f ( 2 h - v ) ) + q + t + g ( 2 h - v ) ( p + s + f ( 2 h - v ) ) - 2 n - 2 i = 0 n l = 0 i ( - 1 ) i - l 4 i ( a + c ( 2 h - v ) + w ) - i - l + 2 n ( a + c ( 2 h - v ) + w + 2 ( p + s + f ( 2 h - v ) ) z ) i + l ( - ( a + c ( 2 h - v ) + w + 2 ( p + s + f ( 2 h - v ) ) z ) 2 p + s + f ( 2 h - v ) ) 1 2 ( - i - l - 1 ) ( i l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity, Rule[Editable, True]]], List[TagBox["l", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["i", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( ( a + c ( 2 h - v ) + w ) ( a + c ( 2 h - v ) + w + 2 ( p + s + f ( 2 h - v ) ) z ) Γ ( 1 2 ( i + l + 1 ) , - ( a + c ( 2 h - v ) + w + 2 ( p + s + f ( 2 h - v ) ) z ) 2 4 ( p + s + f ( 2 h - v ) ) ) + 2 ( p + s + f ( 2 h - v ) ) Γ ( 1 2 ( i + l + 2 ) , - ( a + c ( 2 h - v ) + w + 2 ( p + s + f ( 2 h - v ) ) z ) 2 4 ( p + s + f ( 2 h - v ) ) ) - ( a + c ( 2 h - v ) + w + 2 ( p + s + f ( 2 h - v ) ) z ) 2 p + s + f ( 2 h - v ) ) - - ( - a + c ( v - 2 h ) - w ) 2 4 ( - p - s + f ( v - 2 h ) ) - q - t + g ( v - 2 h ) ( - p - s + f ( v - 2 h ) ) - 2 n - 2 i = 0 n l = 0 i ( - 1 ) i - l 4 i ( - a + c ( v - 2 h ) - w ) - i - l + 2 n ( - a + c ( v - 2 h ) - w + 2 ( - p - s + f ( v - 2 h ) ) z ) i + l ( - ( - a + c ( v - 2 h ) - w + 2 ( - p - s + f ( v - 2 h ) ) z ) 2 - p - s + f ( v - 2 h ) ) 1 2 ( - i - l - 1 ) ( i l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity, Rule[Editable, True]]], List[TagBox["l", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["i", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( ( - a + c ( v - 2 h ) - w ) ( - a + c ( v - 2 h ) - w + 2 ( - p - s + f ( v - 2 h ) ) z ) Γ ( 1 2 ( i + l + 1 ) , - ( - a + c ( v - 2 h ) - w + 2 ( - p - s + f ( v - 2 h ) ) z ) 2 4 ( - p - s + f ( v - 2 h ) ) ) + 2 ( - p - s + f ( v - 2 h ) ) Γ ( 1 2 ( i + l + 2 ) , - ( - a + c ( v - 2 h ) - w + 2 ( - p - s + f ( v - 2 h ) ) z ) 2 4 ( - p - s + f ( v - 2 h ) ) ) - ( - a + c ( v - 2 h ) - w + 2 ( - p - s + f ( v - 2 h ) ) z ) 2 - p - s + f ( v - 2 h ) ) + - ( a + c ( v - 2 h ) - w ) 2 4 ( p - s + f ( v - 2 h ) ) + q - t + g ( v - 2 h ) ( p - s + f ( v - 2 h ) ) - 2 n - 2 i = 0 n l = 0 i ( - 1 ) i - l 4 i ( a + c ( v - 2 h ) - w ) - i - l + 2 n ( a + c ( v - 2 h ) - w + 2 ( p - s + f ( v - 2 h ) ) z ) i + l ( - ( a + c ( v - 2 h ) - w + 2 ( p - s + f ( v - 2 h ) ) z ) 2 p - s + f ( v - 2 h ) ) 1 2 ( - i - l - 1 ) ( i l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity, Rule[Editable, True]]], List[TagBox["l", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["i", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( ( a + c ( v - 2 h ) - w ) ( a + c ( v - 2 h ) - w + 2 ( p - s + f ( v - 2 h ) ) z ) Γ ( 1 2 ( i + l + 1 ) , - ( a + c ( v - 2 h ) - w + 2 ( p - s + f ( v - 2 h ) ) z ) 2 4 ( p - s + f ( v - 2 h ) ) ) + 2 ( p - s + f ( v - 2 h ) ) Γ ( 1 2 ( i + l + 2 ) , - ( a + c ( v - 2 h ) - w + 2 ( p - s + f ( v - 2 h ) ) z ) 2 4 ( p - s + f ( v - 2 h ) ) ) - ( a + c ( v - 2 h ) - w + 2 ( p - s + f ( v - 2 h ) ) z ) 2 p - s + f ( v - 2 h ) ) + - ( - a + c ( v - 2 h ) + w ) 2 4 ( - p + s + f ( v - 2 h ) ) - q + t + g ( v - 2 h ) ( - p + s + f ( v - 2 h ) ) - 2 n - 2 i = 0 n l = 0 i ( - 1 ) i - l 4 i ( - a + c ( v - 2 h ) + w ) - i - l + 2 n ( - a + c ( v - 2 h ) + w + 2 ( - p + s + f ( v - 2 h ) ) z ) i + l ( - ( - a + c ( v - 2 h ) + w + 2 ( - p + s + f ( v - 2 h ) ) z ) 2 - p + s + f ( v - 2 h ) ) 1 2 ( - i - l - 1 ) ( i l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity, Rule[Editable, True]]], List[TagBox["l", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["i", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( ( - a + c ( v - 2 h ) + w ) ( - a + c ( v - 2 h ) + w + 2 ( - p + s + f ( v - 2 h ) ) z ) Γ ( 1 2 ( i + l + 1 ) , - ( - a + c ( v - 2 h ) + w + 2 ( - p + s + f ( v - 2 h ) ) z ) 2 4 ( - p + s + f ( v - 2 h ) ) ) + 2 ( - p + s + f ( v - 2 h ) ) Γ ( 1 2 ( i + l + 2 ) , - ( - a + c ( v - 2 h ) + w + 2 ( - p + s + f ( v - 2 h ) ) z ) 2 4 ( - p + s + f ( v - 2 h ) ) ) - ( - a + c ( v - 2 h ) + w + 2 ( - p + s + f ( v - 2 h ) ) z ) 2 - p + s + f ( v - 2 h ) ) - - ( a + c ( v - 2 h ) + w ) 2 4 ( p + s + f ( v - 2 h ) ) + q + t + g ( v - 2 h ) ( p + s + f ( v - 2 h ) ) - 2 n - 2 i = 0 n l = 0 i ( - 1 ) i - l 4 i ( a + c ( v - 2 h ) + w ) - i - l + 2 n ( a + c ( v - 2 h ) + w + 2 ( p + s + f ( v - 2 h ) ) z ) i + l ( - ( a + c ( v - 2 h ) + w + 2 ( p + s + f ( v - 2 h ) ) z ) 2 p + s + f ( v - 2 h ) ) 1 2 ( - i - l - 1 ) ( i l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity, Rule[Editable, True]]], List[TagBox["l", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["i", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( ( a + c ( v - 2 h ) + w ) ( a + c ( v - 2 h ) + w + 2 ( p + s + f ( v - 2 h ) ) z ) Γ ( 1 2 ( i + l + 1 ) , - ( a + c ( v - 2 h ) + w + 2 ( p + s + f ( v - 2 h ) ) z ) 2 4 ( p + s + f ( v - 2 h ) ) ) + 2 ( p + s + f ( v - 2 h ) ) Γ ( 1 2 ( i + l + 2 ) , - ( a + c ( v - 2 h ) + w + 2 ( p + s + f ( v - 2 h ) ) z ) 2 4 ( p + s + f ( v - 2 h ) ) ) - ( a + c ( v - 2 h ) + w + 2 ( p + s + f ( v - 2 h ) ) z ) 2 p + s + f ( v - 2 h ) ) ) /; n v TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] v > 0 Condition z z n z 1 2 a q p z t s z w z 1 2 z 1 2 c g f z v 2 -2 n -1 v -3 Binomial v v 2 -1 1 -1 \$CellContext`v 2 -1 -1 -1 a -1 w 2 4 -1 p -1 s -1 -1 q -1 t l 0 i i 0 n -1 i -1 l 4 i -1 a -1 w -1 i -1 l 2 n -1 a -1 w 2 -1 p -1 s z 1 2 i l -1 -1 a -1 w 2 -1 p -1 s z 1 2 2 -1 p -1 s -1 1 2 -1 i -1 l -1 Binomial i l Binomial n i -1 a -1 w -1 a -1 w 2 -1 p -1 s z 1 2 Gamma 1 2 i l 1 -1 -1 a -1 w 2 -1 p -1 s z 1 2 2 4 -1 p -1 s -1 2 -1 -1 a -1 w 2 -1 p -1 s z 1 2 2 -1 p -1 s -1 1 2 -1 p -1 s Gamma 1 2 i l 2 -1 -1 a -1 w 2 -1 p -1 s z 1 2 2 4 -1 p -1 s -1 -1 p -1 s -2 n -2 -1 a -1 w 2 4 p -1 s -1 q -1 t p -1 s -2 n -2 l 0 i i 0 n -1 i -1 l 4 i a -1 w -1 i -1 l 2 n a -1 w 2 p -1 s z 1 2 i l -1 a -1 w 2 p -1 s z 1 2 2 p -1 s -1 1 2 -1 i -1 l -1 Binomial i l Binomial n i a -1 w a -1 w 2 p -1 s z 1 2 Gamma 1 2 i l 1 -1 a -1 w 2 p -1 s z 1 2 2 4 p -1 s -1 2 -1 a -1 w 2 p -1 s z 1 2 2 p -1 s -1 1 2 p -1 s Gamma 1 2 i l 2 -1 a -1 w 2 p -1 s z 1 2 2 4 p -1 s -1 -1 -1 a w 2 4 s -1 p -1 -1 q t s -1 p -2 n -2 l 0 i i 0 n -1 i -1 l 4 i -1 a w -1 i -1 l 2 n -1 a w 2 s -1 p z 1 2 i l -1 -1 a w 2 s -1 p z 1 2 2 s -1 p -1 1 2 -1 i -1 l -1 Binomial i l Binomial n i -1 a w -1 a w 2 s -1 p z 1 2 Gamma 1 2 i l 1 -1 -1 a w 2 s -1 p z 1 2 2 4 s -1 p -1 2 -1 -1 a w 2 s -1 p z 1 2 2 s -1 p -1 1 2 s -1 p Gamma 1 2 i l 2 -1 -1 a w 2 s -1 p z 1 2 2 4 s -1 p -1 -1 -1 a w 2 4 p s -1 q t p s -2 n -2 l 0 i i 0 n -1 i -1 l 4 i a w -1 i -1 l 2 n a w 2 p s z 1 2 i l -1 a w 2 p s z 1 2 2 p s -1 1 2 -1 i -1 l -1 Binomial i l Binomial n i a w a w 2 p s z 1 2 Gamma 1 2 i l 1 -1 a w 2 p s z 1 2 2 4 p s -1 2 -1 a w 2 p s z 1 2 2 p s -1 1 2 p s Gamma 1 2 i l 2 -1 a w 2 p s z 1 2 2 4 p s -1 2 -2 n -1 v -3 h 0 v -1 2 -1 Binomial v h -1 -1 -1 a c 2 h -1 v -1 w 2 4 -1 p -1 s f 2 h -1 v -1 -1 q -1 t g 2 h -1 v l 0 i i 0 n -1 i -1 l 4 i -1 a c 2 h -1 v -1 w -1 i -1 l 2 n -1 a c 2 h -1 v -1 w 2 -1 p -1 s f 2 h -1 v z 1 2 i l -1 -1 a c 2 h -1 v -1 w 2 -1 p -1 s f 2 h -1 v z 1 2 2 -1 p -1 s f 2 h -1 v -1 1 2 -1 i -1 l -1 Binomial i l Binomial n i -1 a c 2 h -1 v -1 w -1 a c 2 h -1 v -1 w 2 -1 p -1 s f 2 h -1 v z 1 2 Gamma 1 2 i l 1 -1 -1 a c 2 h -1 v -1 w 2 -1 p -1 s f 2 h -1 v z 1 2 2 4 -1 p -1 s f 2 h -1 v -1 2 -1 p -1 s f 2 h -1 v Gamma 1 2 i l 2 -1 -1 a c 2 h -1 v -1 w 2 -1 p -1 s f 2 h -1 v z 1 2 2 4 -1 p -1 s f 2 h -1 v -1 -1 -1 a c 2 h -1 v -1 w 2 -1 p -1 s f 2 h -1 v z 1 2 2 -1 p -1 s f 2 h -1 v -1 1 2 -1 p -1 s f 2 h -1 v -2 n -2 -1 a c 2 h -1 v -1 w 2 4 p -1 s f 2 h -1 v -1 q -1 t g 2 h -1 v p -1 s f 2 h -1 v -2 n -2 l 0 i i 0 n -1 i -1 l 4 i a c 2 h -1 v -1 w -1 i -1 l 2 n a c 2 h -1 v -1 w 2 p -1 s f 2 h -1 v z 1 2 i l -1 a c 2 h -1 v -1 w 2 p -1 s f 2 h -1 v z 1 2 2 p -1 s f 2 h -1 v -1 1 2 -1 i -1 l -1 Binomial i l Binomial n i a c 2 h -1 v -1 w a c 2 h -1 v -1 w 2 p -1 s f 2 h -1 v z 1 2 Gamma 1 2 i l 1 -1 a c 2 h -1 v -1 w 2 p -1 s f 2 h -1 v z 1 2 2 4 p -1 s f 2 h -1 v -1 2 p -1 s f 2 h -1 v Gamma 1 2 i l 2 -1 a c 2 h -1 v -1 w 2 p -1 s f 2 h -1 v z 1 2 2 4 p -1 s f 2 h -1 v -1 -1 a c 2 h -1 v -1 w 2 p -1 s f 2 h -1 v z 1 2 2 p -1 s f 2 h -1 v -1 1 2 -1 -1 a c 2 h -1 v w 2 4 -1 p s f 2 h -1 v -1 -1 q t g 2 h -1 v -1 p s f 2 h -1 v -2 n -2 l 0 i i 0 n -1 i -1 l 4 i -1 a c 2 h -1 v w -1 i -1 l 2 n -1 a c 2 h -1 v w 2 -1 p s f 2 h -1 v z 1 2 i l -1 -1 a c 2 h -1 v w 2 -1 p s f 2 h -1 v z 1 2 2 -1 p s f 2 h -1 v -1 1 2 -1 i -1 l -1 Binomial i l Binomial n i -1 a c 2 h -1 v w -1 a c 2 h -1 v w 2 -1 p s f 2 h -1 v z 1 2 Gamma 1 2 i l 1 -1 -1 a c 2 h -1 v w 2 -1 p s f 2 h -1 v z 1 2 2 4 -1 p s f 2 h -1 v -1 2 -1 p s f 2 h -1 v Gamma 1 2 i l 2 -1 -1 a c 2 h -1 v w 2 -1 p s f 2 h -1 v z 1 2 2 4 -1 p s f 2 h -1 v -1 -1 -1 a c 2 h -1 v w 2 -1 p s f 2 h -1 v z 1 2 2 -1 p s f 2 h -1 v -1 1 2 -1 -1 a c 2 h -1 v w 2 4 p s f 2 h -1 v -1 q t g 2 h -1 v p s f 2 h -1 v -2 n -2 l 0 i i 0 n -1 i -1 l 4 i a c 2 h -1 v w -1 i -1 l 2 n a c 2 h -1 v w 2 p s f 2 h -1 v z 1 2 i l -1 a c 2 h -1 v w 2 p s f 2 h -1 v z 1 2 2 p s f 2 h -1 v -1 1 2 -1 i -1 l -1 Binomial i l Binomial n i a c 2 h -1 v w a c 2 h -1 v w 2 p s f 2 h -1 v z 1 2 Gamma 1 2 i l 1 -1 a c 2 h -1 v w 2 p s f 2 h -1 v z 1 2 2 4 p s f 2 h -1 v -1 2 p s f 2 h -1 v Gamma 1 2 i l 2 -1 a c 2 h -1 v w 2 p s f 2 h -1 v z 1 2 2 4 p s f 2 h -1 v -1 -1 a c 2 h -1 v w 2 p s f 2 h -1 v z 1 2 2 p s f 2 h -1 v -1 1 2 -1 -1 -1 a c v -1 2 h -1 w 2 4 -1 p -1 s f v -1 2 h -1 -1 q -1 t g v -1 2 h -1 p -1 s f v -1 2 h -2 n -2 l 0 i i 0 n -1 i -1 l 4 i -1 a c v -1 2 h -1 w -1 i -1 l 2 n -1 a c v -1 2 h -1 w 2 -1 p -1 s f v -1 2 h z 1 2 i l -1 -1 a c v -1 2 h -1 w 2 -1 p -1 s f v -1 2 h z 1 2 2 -1 p -1 s f v -1 2 h -1 1 2 -1 i -1 l -1 Binomial i l Binomial n i -1 a c v -1 2 h -1 w -1 a c v -1 2 h -1 w 2 -1 p -1 s f v -1 2 h z 1 2 Gamma 1 2 i l 1 -1 -1 a c v -1 2 h -1 w 2 -1 p -1 s f v -1 2 h z 1 2 2 4 -1 p -1 s f v -1 2 h -1 2 -1 p -1 s f v -1 2 h Gamma 1 2 i l 2 -1 -1 a c v -1 2 h -1 w 2 -1 p -1 s f v -1 2 h z 1 2 2 4 -1 p -1 s f v -1 2 h -1 -1 -1 a c v -1 2 h -1 w 2 -1 p -1 s f v -1 2 h z 1 2 2 -1 p -1 s f v -1 2 h -1 1 2 -1 a c v -1 2 h -1 w 2 4 p -1 s f v -1 2 h -1 q -1 t g v -1 2 h p -1 s f v -1 2 h -2 n -2 l 0 i i 0 n -1 i -1 l 4 i a c v -1 2 h -1 w -1 i -1 l 2 n a c v -1 2 h -1 w 2 p -1 s f v -1 2 h z 1 2 i l -1 a c v -1 2 h -1 w 2 p -1 s f v -1 2 h z 1 2 2 p -1 s f v -1 2 h -1 1 2 -1 i -1 l -1 Binomial i l Binomial n i a c v -1 2 h -1 w a c v -1 2 h -1 w 2 p -1 s f v -1 2 h z 1 2 Gamma 1 2 i l 1 -1 a c v -1 2 h -1 w 2 p -1 s f v -1 2 h z 1 2 2 4 p -1 s f v -1 2 h -1 2 p -1 s f v -1 2 h Gamma 1 2 i l 2 -1 a c v -1 2 h -1 w 2 p -1 s f v -1 2 h z 1 2 2 4 p -1 s f v -1 2 h -1 -1 a c v -1 2 h -1 w 2 p -1 s f v -1 2 h z 1 2 2 p -1 s f v -1 2 h -1 1 2 -1 -1 a c v -1 2 h w 2 4 -1 p s f v -1 2 h -1 -1 q t g v -1 2 h -1 p s f v -1 2 h -2 n -2 l 0 i i 0 n -1 i -1 l 4 i -1 a c v -1 2 h w -1 i -1 l 2 n -1 a c v -1 2 h w 2 -1 p s f v -1 2 h z 1 2 i l -1 -1 a c v -1 2 h w 2 -1 p s f v -1 2 h z 1 2 2 -1 p s f v -1 2 h -1 1 2 -1 i -1 l -1 Binomial i l Binomial n i -1 a c v -1 2 h w -1 a c v -1 2 h w 2 -1 p s f v -1 2 h z 1 2 Gamma 1 2 i l 1 -1 -1 a c v -1 2 h w 2 -1 p s f v -1 2 h z 1 2 2 4 -1 p s f v -1 2 h -1 2 -1 p s f v -1 2 h Gamma 1 2 i l 2 -1 -1 a c v -1 2 h w 2 -1 p s f v -1 2 h z 1 2 2 4 -1 p s f v -1 2 h -1 -1 -1 a c v -1 2 h w 2 -1 p s f v -1 2 h z 1 2 2 -1 p s f v -1 2 h -1 1 2 -1 -1 a c v -1 2 h w 2 4 p s f v -1 2 h -1 q t g v -1 2 h p s f v -1 2 h -2 n -2 l 0 i i 0 n -1 i -1 l 4 i a c v -1 2 h w -1 i -1 l 2 n a c v -1 2 h w 2 p s f v -1 2 h z 1 2 i l -1 a c v -1 2 h w 2 p s f v -1 2 h z 1 2 2 p s f v -1 2 h -1 1 2 -1 i -1 l -1 Binomial i l Binomial n i a c v -1 2 h w a c v -1 2 h w 2 p s f v -1 2 h z 1 2 Gamma 1 2 i l 1 -1 a c v -1 2 h w 2 p s f v -1 2 h z 1 2 2 4 p s f v -1 2 h -1 2 p s f v -1 2 h Gamma 1 2 i l 2 -1 a c v -1 2 h w 2 p s f v -1 2 h z 1 2 2 4 p s f v -1 2 h -1 -1 a c v -1 2 h w 2 p s f v -1 2 h z 1 2 2 p s f v -1 2 h -1 1 2 n v v 0 [/itex]

 Rule Form

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

 2002-12-18