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 Cosh

 http://functions.wolfram.com/01.20.21.4849.01

 Input Form

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

 Standard Form

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")"]]]], "+", RowBox[List["2", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]]]]]]], "]"]]]]]], ")"]]]]]]]]]]]], ")"]]]]]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]], "\[And]", 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 sinh m ( b z ) cosh v ( c z ) z - 2 - m - v + 1 - m p - 2 ( n + 1 ) ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity, Rule[Editable, True]]], List[TagBox[FractionBox["m", "2"], Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( 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]] Γ ( 2 ( n + 1 ) , - p z ) ( 1 - m mod 2 \$CellContext`m 2 ) ( 1 - v mod 2 \$CellContext`v 2 ) - 2 - m - v + 1 - m ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity, Rule[Editable, True]]], List[TagBox[FractionBox["m", "2"], Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( 1 - m mod 2 \$CellContext`m 2 ) s = 0 v - 1 2 ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity, Rule[Editable, True]]], List[TagBox["s", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( Γ ( 2 ( n + 1 ) , ( c ( v - 2 s ) - p ) z ) ( c ( v - 2 s ) - p ) - 2 ( n + 1 ) + ( p + c ( v - 2 s ) ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( - p - c ( v - 2 s ) ) z ) ) + 2 - m - 2 n - v - 1 ( 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 ) k = 0 m - 1 2 ( - 1 ) k ( - b ( m - 2 k ) ) - 2 ( n + 1 ) ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity, Rule[Editable, True]]], List[TagBox["k", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( ( - 1 ) m p 2 4 b ( m - 2 k ) i = 0 n h = 0 i ( - 1 ) i - h 4 i p - h - i + 2 n ( p - 2 b ( m - 2 k ) z ) h + i ( ( p - 2 b ( m - 2 k ) z ) 2 b ( m - 2 k ) ) 1 2 ( - h - i - 1 ) ( i h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity, Rule[Editable, True]]], List[TagBox["h", 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]] ( p ( p - 2 b ( m - 2 k ) z ) Γ ( 1 2 ( h + i + 1 ) , ( p - 2 b ( m - 2 k ) z ) 2 4 b ( m - 2 k ) ) - 2 b ( m - 2 k ) ( p - 2 b ( m - 2 k ) z ) 2 b ( m - 2 k ) Γ ( 1 2 ( h + i + 2 ) , ( p - 2 b ( m - 2 k ) z ) 2 4 b ( m - 2 k ) ) ) + - p 2 4 b ( m - 2 k ) i = 0 n h = 0 i ( - 1 ) i - h 4 i p - h - i + 2 n ( 2 b z ( m - 2 k ) + p ) h + i ( - ( 2 b z ( m - 2 k ) + p ) 2 b ( m - 2 k ) ) 1 2 ( - h - i - 1 ) ( i h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity, Rule[Editable, True]]], List[TagBox["h", 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]] ( p ( 2 b z ( m - 2 k ) + p ) Γ ( 1 2 ( h + i + 1 ) , - ( 2 b z ( m - 2 k ) + p ) 2 4 b ( m - 2 k ) ) + 2 b ( m - 2 k ) - ( 2 b z ( m - 2 k ) + p ) 2 b ( m - 2 k ) Γ ( 1 2 ( h + i + 2 ) , - ( 2 b z ( m - 2 k ) + p ) 2 4 b ( m - 2 k ) ) ) ) + 2 - m - 2 n - v - 1 - m k = 0 m - 1 2 ( - 1 ) k ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity, Rule[Editable, True]]], List[TagBox["k", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] s = 0 v - 1 2 ( - b ( m - 2 k ) ) - 2 ( n + 1 ) ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity, Rule[Editable, True]]], List[TagBox["s", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( ( p + c ( v - 2 s ) ) 2 4 b ( m - 2 k ) - m π 2 i = 0 n h = 0 i ( - 1 ) i - h 4 i ( p + c ( v - 2 s ) ) - h - i + 2 n ( - 2 b z ( m - 2 k ) + p + c ( v - 2 s ) ) h + i ( ( - 2 b z ( m - 2 k ) + p + c ( v - 2 s ) ) 2 b ( m - 2 k ) ) 1 2 ( - h - i - 1 ) ( i h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity, Rule[Editable, True]]], List[TagBox["h", 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]] ( ( p + c ( v - 2 s ) ) ( - 2 b z ( m - 2 k ) + p + c ( v - 2 s ) ) Γ ( 1 2 ( h + i + 1 ) , ( - 2 b z ( m - 2 k ) + p + c ( v - 2 s ) ) 2 4 b ( m - 2 k ) ) - 2 b ( m - 2 k ) ( - 2 b z ( m - 2 k ) + p + c ( v - 2 s ) ) 2 b ( m - 2 k ) Γ ( 1 2 ( h + i + 2 ) , ( - 2 b z ( m - 2 k ) + p + c ( v - 2 s ) ) 2 4 b ( m - 2 k ) ) ) + ( p - c ( v - 2 s ) ) 2 4 b ( m - 2 k ) - m π 2 i = 0 n h = 0 i ( - 1 ) i - h 4 i ( p - c ( v - 2 s ) ) - h - i + 2 n ( - 2 b z ( m - 2 k ) + p - c ( v - 2 s ) ) h + i ( ( - 2 b z ( m - 2 k ) + p - c ( v - 2 s ) ) 2 b ( m - 2 k ) ) 1 2 ( - h - i - 1 ) ( i h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity, Rule[Editable, True]]], List[TagBox["h", 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]] ( ( p - c ( v - 2 s ) ) ( - 2 b z ( m - 2 k ) + p - c ( v - 2 s ) ) Γ ( 1 2 ( h + i + 1 ) , ( - 2 b z ( m - 2 k ) + p - c ( v - 2 s ) ) 2 4 b ( m - 2 k ) ) - 2 b ( m - 2 k ) ( - 2 b z ( m - 2 k ) + p - c ( v - 2 s ) ) 2 b ( m - 2 k ) Γ ( 1 2 ( h + i + 2 ) , ( - 2 b z ( m - 2 k ) + p - c ( v - 2 s ) ) 2 4 b ( m - 2 k ) ) ) + m π 2 - ( p + c ( v - 2 s ) ) 2 4 b ( m - 2 k ) i = 0 n h = 0 i ( - 1 ) i - h 4 i ( p + c ( v - 2 s ) ) - h - i + 2 n ( 2 b z ( m - 2 k ) + p + c ( v - 2 s ) ) h + i ( - ( 2 b z ( m - 2 k ) + p + c ( v - 2 s ) ) 2 b ( m - 2 k ) ) 1 2 ( - h - i - 1 ) ( i h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity, Rule[Editable, True]]], List[TagBox["h", 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]] ( ( p + c ( v - 2 s ) ) ( 2 b z ( m - 2 k ) + p + c ( v - 2 s ) ) Γ ( 1 2 ( h + i + 1 ) , - ( 2 b z ( m - 2 k ) + p + c ( v - 2 s ) ) 2 4 b ( m - 2 k ) ) + 2 b ( m - 2 k ) - ( 2 b z ( m - 2 k ) + p + c ( v - 2 s ) ) 2 b ( m - 2 k ) Γ ( 1 2 ( h + i + 2 ) , - ( 2 b z ( m - 2 k ) + p + c ( v - 2 s ) ) 2 4 b ( m - 2 k ) ) ) + m π 2 - ( p - c ( v - 2 s ) ) 2 4 b ( m - 2 k ) i = 0 n h = 0 i ( - 1 ) i - h 4 i ( p - c ( v - 2 s ) ) - h - i + 2 n ( 2 b z ( m - 2 k ) + p - c ( v - 2 s ) ) h + i ( - ( 2 b z ( m - 2 k ) + p - c ( v - 2 s ) ) 2 b ( m - 2 k ) ) 1 2 ( - h - i - 1 ) ( i h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity, Rule[Editable, True]]], List[TagBox["h", 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]] ( ( p - c ( v - 2 s ) ) ( 2 b z ( m - 2 k ) + p - c ( v - 2 s ) ) Γ ( 1 2 ( h + i + 1 ) , - ( 2 b z ( m - 2 k ) + p - c ( v - 2 s ) ) 2 4 b ( m - 2 k ) ) + 2 b ( m - 2 k ) - ( 2 b z ( m - 2 k ) + p - c ( v - 2 s ) ) 2 b ( m - 2 k ) Γ ( 1 2 ( h + i + 2 ) , - ( 2 b z ( m - 2 k ) + p - c ( v - 2 s ) ) 2 4 b ( m - 2 k ) ) ) ) /; m + v + n Condition z z n p z 1 2 b z m c z 1 2 v -1 2 -1 m -1 v 1 -1 m p -2 n 1 Binomial m m 2 -1 Binomial v v 2 -1 Gamma 2 n 1 -1 p z 1 2 1 -1 \$CellContext`m 2 1 -1 \$CellContext`v 2 -1 2 -1 m -1 v 1 -1 m Binomial m m 2 -1 1 -1 \$CellContext`m 2 s 0 v -1 2 -1 Binomial v s Gamma 2 n 1 c v -1 2 s -1 p z 1 2 c v -1 2 s -1 p -2 n 1 p c v -1 2 s -2 n 1 Gamma 2 n 1 -1 p -1 c v -1 2 s z 1 2 2 -1 m -1 2 n -1 v -1 Binomial v v 2 -1 1 -1 \$CellContext`v 2 k 0 m -1 2 -1 -1 k -1 b m -1 2 k -2 n 1 Binomial m k -1 m p 2 4 b m -1 2 k -1 h 0 i i 0 n -1 i -1 h 4 i p -1 h -1 i 2 n p -1 2 b m -1 2 k z 1 2 h i p -1 2 b m -1 2 k z 1 2 2 b m -1 2 k -1 1 2 -1 h -1 i -1 Binomial i h Binomial n i p p -1 2 b m -1 2 k z 1 2 Gamma 1 2 h i 1 p -1 2 b m -1 2 k z 1 2 2 4 b m -1 2 k -1 -1 2 b m -1 2 k p -1 2 b m -1 2 k z 1 2 2 b m -1 2 k -1 1 2 Gamma 1 2 h i 2 p -1 2 b m -1 2 k z 1 2 2 4 b m -1 2 k -1 -1 p 2 4 b m -1 2 k -1 h 0 i i 0 n -1 i -1 h 4 i p -1 h -1 i 2 n 2 b z 1 2 m -1 2 k p h i -1 2 b z 1 2 m -1 2 k p 2 b m -1 2 k -1 1 2 -1 h -1 i -1 Binomial i h Binomial n i p 2 b z 1 2 m -1 2 k p Gamma 1 2 h i 1 -1 2 b z 1 2 m -1 2 k p 2 4 b m -1 2 k -1 2 b m -1 2 k -1 2 b z 1 2 m -1 2 k p 2 b m -1 2 k -1 1 2 Gamma 1 2 h i 2 -1 2 b z 1 2 m -1 2 k p 2 4 b m -1 2 k -1 2 -1 m -1 2 n -1 v -1 -1 m k 0 m -1 2 -1 -1 k Binomial m k s 0 v -1 2 -1 -1 b m -1 2 k -2 n 1 Binomial v s p c v -1 2 s 2 4 b m -1 2 k -1 -1 m 2 -1 h 0 i i 0 n -1 i -1 h 4 i p c v -1 2 s -1 h -1 i 2 n -2 b z 1 2 m -1 2 k p c v -1 2 s h i -2 b z 1 2 m -1 2 k p c v -1 2 s 2 b m -1 2 k -1 1 2 -1 h -1 i -1 Binomial i h Binomial n i p c v -1 2 s -2 b z 1 2 m -1 2 k p c v -1 2 s Gamma 1 2 h i 1 -2 b z 1 2 m -1 2 k p c v -1 2 s 2 4 b m -1 2 k -1 -1 2 b m -1 2 k -2 b z 1 2 m -1 2 k p c v -1 2 s 2 b m -1 2 k -1 1 2 Gamma 1 2 h i 2 -2 b z 1 2 m -1 2 k p c v -1 2 s 2 4 b m -1 2 k -1 p -1 c v -1 2 s 2 4 b m -1 2 k -1 -1 m 2 -1 h 0 i i 0 n -1 i -1 h 4 i p -1 c v -1 2 s -1 h -1 i 2 n -2 b z 1 2 m -1 2 k p -1 c v -1 2 s h i -2 b z 1 2 m -1 2 k p -1 c v -1 2 s 2 b m -1 2 k -1 1 2 -1 h -1 i -1 Binomial i h Binomial n i p -1 c v -1 2 s -2 b z 1 2 m -1 2 k p -1 c v -1 2 s Gamma 1 2 h i 1 -2 b z 1 2 m -1 2 k p -1 c v -1 2 s 2 4 b m -1 2 k -1 -1 2 b m -1 2 k -2 b z 1 2 m -1 2 k p -1 c v -1 2 s 2 b m -1 2 k -1 1 2 Gamma 1 2 h i 2 -2 b z 1 2 m -1 2 k p -1 c v -1 2 s 2 4 b m -1 2 k -1 m 2 -1 -1 p c v -1 2 s 2 4 b m -1 2 k -1 h 0 i i 0 n -1 i -1 h 4 i p c v -1 2 s -1 h -1 i 2 n 2 b z 1 2 m -1 2 k p c v -1 2 s h i -1 2 b z 1 2 m -1 2 k p c v -1 2 s 2 b m -1 2 k -1 1 2 -1 h -1 i -1 Binomial i h Binomial n i p c v -1 2 s 2 b z 1 2 m -1 2 k p c v -1 2 s Gamma 1 2 h i 1 -1 2 b z 1 2 m -1 2 k p c v -1 2 s 2 4 b m -1 2 k -1 2 b m -1 2 k -1 2 b z 1 2 m -1 2 k p c v -1 2 s 2 b m -1 2 k -1 1 2 Gamma 1 2 h i 2 -1 2 b z 1 2 m -1 2 k p c v -1 2 s 2 4 b m -1 2 k -1 m 2 -1 -1 p -1 c v -1 2 s 2 4 b m -1 2 k -1 h 0 i i 0 n -1 i -1 h 4 i p -1 c v -1 2 s -1 h -1 i 2 n 2 b z 1 2 m -1 2 k p -1 c v -1 2 s h i -1 2 b z 1 2 m -1 2 k p -1 c v -1 2 s 2 b m -1 2 k -1 1 2 -1 h -1 i -1 Binomial i h Binomial n i p -1 c v -1 2 s 2 b z 1 2 m -1 2 k p -1 c v -1 2 s Gamma 1 2 h i 1 -1 2 b z 1 2 m -1 2 k p -1 c v -1 2 s 2 4 b m -1 2 k -1 2 b m -1 2 k -1 2 b z 1 2 m -1 2 k p -1 c v -1 2 s 2 b m -1 2 k -1 1 2 Gamma 1 2 h i 2 -1 2 b z 1 2 m -1 2 k p -1 c v -1 2 s 2 4 b m -1 2 k -1 m SuperPlus v SuperPlus n [/itex]

 Rule Form

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

 2002-12-18