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/01.20.21.3962.01

 Input Form

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

 Standard Form

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RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], "/", RowBox[List["(", RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]]]], ")"]]]]]]]], "]"]]]]]]]]]], ")"]]]]]]]]]]]]]]]], "/;", 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 b z 2 + d z + e sin m ( a z 2 + p z + q ) cosh v ( c z 2 + f z + g ) z - 2 - m - v - 1 e - d 2 4 b ( 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]]]]] ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox[FractionBox["v", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 - m mod 2 \$CellContext`m 2 ) ( 1 - v mod 2 \$CellContext`v 2 ) b - n - 1 j = 0 n 2 j - n ( - d ) n - j ( d + 2 b z ) j + 1 ( - ( d + 2 b z ) 2 b ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d + 2 b z ) 2 4 b ) - 2 - m - v - 1 ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox[FractionBox["v", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 - v mod 2 \$CellContext`v 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]]]]] ( - ( d + ( 2 k - m ) p ) 2 4 ( b + a ( 2 k - m ) ) + e + ( 2 k - m ) q + m π 2 ( b + a ( 2 k - m ) ) - n - 1 j = 0 n 2 j - n ( - d - ( 2 k - m ) p ) n - j ( d + ( 2 k - m ) p + 2 ( b + a ( 2 k - m ) ) z ) j + 1 ( - ( d + ( 2 k - m ) p + 2 ( b + a ( 2 k - m ) ) z ) 2 b + a ( 2 k - m ) ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d + ( 2 k - m ) p + 2 ( b + a ( 2 k - m ) ) z ) 2 4 ( b + a ( 2 k - m ) ) ) + - ( d + ( m - 2 k ) p ) 2 4 ( b + a ( m - 2 k ) ) + e + ( m - 2 k ) q - m π 2 ( b + a ( m - 2 k ) ) - n - 1 j = 0 n 2 j - n ( - d - ( m - 2 k ) p ) n - j ( d + ( m - 2 k ) p + 2 ( b + a ( m - 2 k ) ) z ) j + 1 ( - ( d + ( m - 2 k ) p + 2 ( b + a ( m - 2 k ) ) z ) 2 b + a ( m - 2 k ) ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d + ( m - 2 k ) p + 2 ( b + a ( m - 2 k ) ) z ) 2 4 ( b + a ( m - 2 k ) ) ) ) - 2 - m - v - 1 ( 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]]]]] ( 1 - m mod 2 \$CellContext`m 2 ) s = 0 v - 1 2 ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - ( d + f ( 2 s - v ) ) 2 4 ( b + c ( 2 s - v ) ) + e + g ( 2 s - v ) ( b + c ( 2 s - v ) ) - n - 1 j = 0 n 2 j - n ( - d - f ( 2 s - v ) ) n - j ( d + f ( 2 s - v ) + 2 ( b + c ( 2 s - v ) ) z ) j + 1 ( - ( d + f ( 2 s - v ) + 2 ( b + c ( 2 s - v ) ) z ) 2 b + c ( 2 s - v ) ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d + f ( 2 s - v ) + 2 ( b + c ( 2 s - v ) ) z ) 2 4 ( b + c ( 2 s - v ) ) ) + - ( d + f ( v - 2 s ) ) 2 4 ( b + c ( v - 2 s ) ) + e + g ( v - 2 s ) ( b + c ( v - 2 s ) ) - n - 1 j = 0 n 2 j - n ( - d - f ( v - 2 s ) ) n - j ( d + f ( v - 2 s ) + 2 ( b + c ( v - 2 s ) ) z ) j + 1 ( - ( d + f ( v - 2 s ) + 2 ( b + c ( v - 2 s ) ) z ) 2 b + c ( v - 2 s ) ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d + f ( v - 2 s ) + 2 ( b + c ( v - 2 s ) ) z ) 2 4 ( b + c ( v - 2 s ) ) ) ) - 2 - m - v - 1 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]]]]] s = 0 v - 1 2 ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - ( d + ( 2 k - m ) p + f ( 2 s - v ) ) 2 4 ( b + a ( 2 k - m ) + c ( 2 s - v ) ) + e + ( 2 k - m ) q + g ( 2 s - v ) + m π 2 ( b + a ( 2 k - m ) + c ( 2 s - v ) ) - n - 1 j = 0 n 2 j - n ( - d - ( 2 k - m ) p - f ( 2 s - v ) ) n - j ( d + ( 2 k - m ) p + f ( 2 s - v ) + 2 ( b + a ( 2 k - m ) + c ( 2 s - v ) ) z ) j + 1 ( - ( d + ( 2 k - m ) p + f ( 2 s - v ) + 2 ( b + a ( 2 k - m ) + c ( 2 s - v ) ) z ) 2 / ( b + a ( 2 k - m ) + c ( 2 s - v ) ) ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d + ( 2 k - m ) p + f ( 2 s - v ) + 2 ( b + a ( 2 k - m ) + c ( 2 s - v ) ) z ) 2 / ( 4 ( b + a ( 2 k - m ) + c ( 2 s - v ) ) ) ) + - ( d + ( m - 2 k ) p + f ( 2 s - v ) ) 2 4 ( b + a ( m - 2 k ) + c ( 2 s - v ) ) + e + ( m - 2 k ) q + g ( 2 s - v ) - m π 2 ( b + a ( m - 2 k ) + c ( 2 s - v ) ) - n - 1 j = 0 n 2 j - n ( - d - ( m - 2 k ) p - f ( 2 s - v ) ) n - j ( d + ( m - 2 k ) p + f ( 2 s - v ) + 2 ( b + a ( m - 2 k ) + c ( 2 s - v ) ) z ) j + 1 ( - ( d + ( m - 2 k ) p + f ( 2 s - v ) + 2 ( b + a ( m - 2 k ) + c ( 2 s - v ) ) z ) 2 / ( b + a ( m - 2 k ) + c ( 2 s - v ) ) ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d + ( m - 2 k ) p + f ( 2 s - v ) + 2 ( b + a ( m - 2 k ) + c ( 2 s - v ) ) z ) 2 / ( 4 ( b + a ( m - 2 k ) + c ( 2 s - v ) ) ) ) + - ( d + ( 2 k - m ) p + f ( v - 2 s ) ) 2 4 ( b + a ( 2 k - m ) + c ( v - 2 s ) ) + e + ( 2 k - m ) q + g ( v - 2 s ) + m π 2 ( b + a ( 2 k - m ) + c ( v - 2 s ) ) - n - 1 j = 0 n 2 j - n ( - d - ( 2 k - m ) p - f ( v - 2 s ) ) n - j ( d + ( 2 k - m ) p + f ( v - 2 s ) + 2 ( b + a ( 2 k - m ) + c ( v - 2 s ) ) z ) j + 1 ( - ( d + ( 2 k - m ) p + f ( v - 2 s ) + 2 ( b + a ( 2 k - m ) + c ( v - 2 s ) ) z ) 2 / ( b + a ( 2 k - m ) + c ( v - 2 s ) ) ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d + ( 2 k - m ) p + f ( v - 2 s ) + 2 ( b + a ( 2 k - m ) + c ( v - 2 s ) ) z ) 2 / ( 4 ( b + a ( 2 k - m ) + c ( v - 2 s ) ) ) ) + - ( d + ( m - 2 k ) p + f ( v - 2 s ) ) 2 4 ( b + a ( m - 2 k ) + c ( v - 2 s ) ) + e + ( m - 2 k ) q + g ( v - 2 s ) - m π 2 ( b + a ( m - 2 k ) + c ( v - 2 s ) ) - n - 1 j = 0 n 2 j - n ( - d - ( m - 2 k ) p - f ( v - 2 s ) ) n - j ( d + ( m - 2 k ) p + f ( v - 2 s ) + 2 ( b + a ( m - 2 k ) + c ( v - 2 s ) ) z ) j + 1 ( - ( d + ( m - 2 k ) p + f ( v - 2 s ) + 2 ( b + a ( m - 2 k ) + c ( v - 2 s ) ) z ) 2 / ( b + a ( m - 2 k ) + c ( v - 2 s ) ) ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d + ( m - 2 k ) p + f ( v - 2 s ) + 2 ( b + a ( m - 2 k ) + c ( v - 2 s ) ) z ) 2 / ( 4 ( b + a ( m - 2 k ) + c ( v - 2 s ) ) ) ) ) /; n m + v + Condition z z n b z 2 d z e a z 2 p z q m c z 2 f z g v -1 2 -1 m -1 v -1 e -1 d 2 4 b -1 Binomial m m 2 -1 Binomial v v 2 -1 1 -1 \$CellContext`m 2 1 -1 \$CellContext`v 2 b -1 n -1 j 0 n 2 j -1 n -1 d n -1 j d 2 b z j 1 -1 d 2 b z 2 b -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d 2 b z 2 4 b -1 -1 2 -1 m -1 v -1 Binomial v v 2 -1 1 -1 \$CellContext`v 2 k 0 m -1 2 -1 -1 k Binomial m k -1 d 2 k -1 m p 2 4 b a 2 k -1 m -1 e 2 k -1 m q m 2 -1 b a 2 k -1 m -1 n -1 j 0 n 2 j -1 n -1 d -1 2 k -1 m p n -1 j d 2 k -1 m p 2 b a 2 k -1 m z j 1 -1 d 2 k -1 m p 2 b a 2 k -1 m z 2 b a 2 k -1 m -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d 2 k -1 m p 2 b a 2 k -1 m z 2 4 b a 2 k -1 m -1 -1 d m -1 2 k p 2 4 b a m -1 2 k -1 e m -1 2 k q -1 m 2 -1 b a m -1 2 k -1 n -1 j 0 n 2 j -1 n -1 d -1 m -1 2 k p n -1 j d m -1 2 k p 2 b a m -1 2 k z j 1 -1 d m -1 2 k p 2 b a m -1 2 k z 2 b a m -1 2 k -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d m -1 2 k p 2 b a m -1 2 k z 2 4 b a m -1 2 k -1 -1 2 -1 m -1 v -1 Binomial m m 2 -1 1 -1 \$CellContext`m 2 s 0 v -1 2 -1 Binomial v s -1 d f 2 s -1 v 2 4 b c 2 s -1 v -1 e g 2 s -1 v b c 2 s -1 v -1 n -1 j 0 n 2 j -1 n -1 d -1 f 2 s -1 v n -1 j d f 2 s -1 v 2 b c 2 s -1 v z j 1 -1 d f 2 s -1 v 2 b c 2 s -1 v z 2 b c 2 s -1 v -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d f 2 s -1 v 2 b c 2 s -1 v z 2 4 b c 2 s -1 v -1 -1 d f v -1 2 s 2 4 b c v -1 2 s -1 e g v -1 2 s b c v -1 2 s -1 n -1 j 0 n 2 j -1 n -1 d -1 f v -1 2 s n -1 j d f v -1 2 s 2 b c v -1 2 s z j 1 -1 d f v -1 2 s 2 b c v -1 2 s z 2 b c v -1 2 s -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d f v -1 2 s 2 b c v -1 2 s z 2 4 b c v -1 2 s -1 -1 2 -1 m -1 v -1 k 0 m -1 2 -1 -1 k Binomial m k s 0 v -1 2 -1 Binomial v s -1 d 2 k -1 m p f 2 s -1 v 2 4 b a 2 k -1 m c 2 s -1 v -1 e 2 k -1 m q g 2 s -1 v m 2 -1 b a 2 k -1 m c 2 s -1 v -1 n -1 j 0 n 2 j -1 n -1 d -1 2 k -1 m p -1 f 2 s -1 v n -1 j d 2 k -1 m p f 2 s -1 v 2 b a 2 k -1 m c 2 s -1 v z j 1 -1 d 2 k -1 m p f 2 s -1 v 2 b a 2 k -1 m c 2 s -1 v z 2 b a 2 k -1 m c 2 s -1 v -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d 2 k -1 m p f 2 s -1 v 2 b a 2 k -1 m c 2 s -1 v z 2 4 b a 2 k -1 m c 2 s -1 v -1 -1 d m -1 2 k p f 2 s -1 v 2 4 b a m -1 2 k c 2 s -1 v -1 e m -1 2 k q g 2 s -1 v -1 m 2 -1 b a m -1 2 k c 2 s -1 v -1 n -1 j 0 n 2 j -1 n -1 d -1 m -1 2 k p -1 f 2 s -1 v n -1 j d m -1 2 k p f 2 s -1 v 2 b a m -1 2 k c 2 s -1 v z j 1 -1 d m -1 2 k p f 2 s -1 v 2 b a m -1 2 k c 2 s -1 v z 2 b a m -1 2 k c 2 s -1 v -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d m -1 2 k p f 2 s -1 v 2 b a m -1 2 k c 2 s -1 v z 2 4 b a m -1 2 k c 2 s -1 v -1 -1 d 2 k -1 m p f v -1 2 s 2 4 b a 2 k -1 m c v -1 2 s -1 e 2 k -1 m q g v -1 2 s m 2 -1 b a 2 k -1 m c v -1 2 s -1 n -1 j 0 n 2 j -1 n -1 d -1 2 k -1 m p -1 f v -1 2 s n -1 j d 2 k -1 m p f v -1 2 s 2 b a 2 k -1 m c v -1 2 s z j 1 -1 d 2 k -1 m p f v -1 2 s 2 b a 2 k -1 m c v -1 2 s z 2 b a 2 k -1 m c v -1 2 s -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d 2 k -1 m p f v -1 2 s 2 b a 2 k -1 m c v -1 2 s z 2 4 b a 2 k -1 m c v -1 2 s -1 -1 d m -1 2 k p f v -1 2 s 2 4 b a m -1 2 k c v -1 2 s -1 e m -1 2 k q g v -1 2 s -1 m 2 -1 b a m -1 2 k c v -1 2 s -1 n -1 j 0 n 2 j -1 n -1 d -1 m -1 2 k p -1 f v -1 2 s n -1 j d m -1 2 k p f v -1 2 s 2 b a m -1 2 k c v -1 2 s z j 1 -1 d m -1 2 k p f v -1 2 s 2 b a m -1 2 k c v -1 2 s z 2 b a m -1 2 k c v -1 2 s -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d m -1 2 k p f v -1 2 s 2 b a m -1 2 k c v -1 2 s z 2 4 b a m -1 2 k c v -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