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; }

 Cos

 http://functions.wolfram.com/01.07.21.2770.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["z", "n"], SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b", " ", SqrtBox["z"]]], "+", RowBox[List["d", " ", "z"]], "+", "e"]]], SuperscriptBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["a", " ", SqrtBox["z"]]], "+", RowBox[List["p", " ", "z"]], "+", "q"]], "]"]], "m"], SuperscriptBox[RowBox[List["Cos", "[", RowBox[List[RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List["f", " ", "z"]], "+", "g"]], "]"]], "v"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "m", "-", RowBox[List["2", " ", "n"]], "-", "v"]]], " ", SuperscriptBox["d", RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]]]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["b", "2"], RowBox[List["4", " ", "d"]]]]]], " ", RowBox[List["(", 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 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", "n_"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b_", " ", SqrtBox["z_"]]], "+", RowBox[List["d_", " ", "z_"]], "+", "e_"]]], " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["a_", " ", SqrtBox["z_"]]], "+", RowBox[List["p_", " ", "z_"]], "+", "q_"]], "]"]], "m_"], " ", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List[RowBox[List["c_", " ", SqrtBox["z_"]]], "+", RowBox[List["f_", " ", "z_"]], "+", "g_"]], "]"]], "v_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "m", "-", RowBox[List["2", " ", "n"]], "-", "v"]]], " ", SuperscriptBox["d", RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]]]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", 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 Date Added to functions.wolfram.com (modification date)

 2002-12-18