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 Cosh

 http://functions.wolfram.com/01.20.21.4013.01

 Input Form

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

 Standard Form

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RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "h", "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["j", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "h", "+", "j"]], ")"]]]], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"]]], RowBox[List["4", " ", "b", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]]], "]"]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]], " ", SqrtBox[FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"]]], RowBox[List["b", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "j"]], ")"]]]], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"]]], RowBox[List["4", " ", "b", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]]], "]"]]]]]], ")"]]]]]]]]]]]], ")"]]]]]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]], "\[And]", RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]], "\[And]", RowBox[List["v", "\[Element]", "Integers"]], "\[And]", RowBox[List["v", ">", "0"]]]]]]]]

 MathML Form

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

 Rule Form

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

 2002-12-18