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 Cosh

 http://functions.wolfram.com/01.20.21.4746.01

 Input Form

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

 Standard Form

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 MathML Form

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+ q + t ( 2 ( a + w + 2 ( p + s ) z ) 2 4 ( p + s ) - ( a + w + 2 ( p + s ) z ) 2 p + s ( p + s ) + ( a + w ) ( a + w + 2 ( p + s ) z ) Γ ( 1 2 , - ( a + w + 2 ( p + s ) z ) 2 4 ( p + s ) ) ) ) / ( ( p + s ) 2 - ( a + w + 2 ( p + s ) z ) 2 p + s ) ) ( 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 ) + 2 - 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 ) ( ( a + c ( 2 h - v ) - w ) ( a + c ( 2 h - v ) - w + 2 ( p - s + f ( 2 h - v ) ) z ) Γ ( 1 2 , - ( a + c ( 2 h - v ) - w + 2 ( p - s + f ( 2 h - v ) ) z ) 2 4 ( p - s + f ( 2 h - v ) ) ) + 2 ( a + c ( 2 h - v ) - w + 2 ( p - s + f ( 2 h - v ) ) z ) 2 4 ( p - s + f ( 2 h - v ) ) ( 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 - ( 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 ) ( ( a + c ( 2 h - v ) + w ) ( a + c ( 2 h - v ) + w + 2 ( p + s + f ( 2 h - v ) ) z ) Γ ( 1 2 , - ( a + c ( 2 h - v ) + w + 2 ( p + s + f ( 2 h - v ) ) z ) 2 4 ( p + s + f ( 2 h - v ) ) ) + 2 ( a + c ( 2 h - v ) + w + 2 ( p + s + f ( 2 h - v ) ) z ) 2 4 ( p + s + f ( 2 h - v ) ) ( 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 - ( 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 ) ( ( - a + c ( 2 h - v ) - w ) ( - a + c ( 2 h - v ) - w + 2 ( - p - s + f ( 2 h - v ) ) z ) Γ ( 1 2 , - ( - a + c ( 2 h - v ) - w + 2 ( - p - s + f ( 2 h - v ) ) z ) 2 4 ( - p - s + f ( 2 h - v ) ) ) + 2 ( - a + c ( 2 h - v ) - w + 2 ( - p - s + f ( 2 h - v ) ) z ) 2 4 ( - p - s + f ( 2 h - v ) ) ( - 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 - ( - 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 ) ( ( - a + c ( 2 h - v ) + w ) ( - a + c ( 2 h - v ) + w + 2 ( - p + s + f ( 2 h - v ) ) z ) Γ ( 1 2 , - ( - a + c ( 2 h - v ) + w + 2 ( - p + s + f ( 2 h - v ) ) z ) 2 4 ( - p + s + f ( 2 h - v ) ) ) + 2 ( - a + c ( 2 h - v ) + w + 2 ( - p + s + f ( 2 h - v ) ) z ) 2 4 ( - p + s + f ( 2 h - v ) ) ( - 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 - ( - 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 ) ( ( - a + c ( v - 2 h ) - w ) ( - a + c ( v - 2 h ) - w + 2 ( - p - s + f ( v - 2 h ) ) z ) Γ ( 1 2 , - ( - a + c ( v - 2 h ) - w + 2 ( - p - s + f ( v - 2 h ) ) z ) 2 4 ( - p - s + f ( v - 2 h ) ) ) + 2 ( - a + c ( v - 2 h ) - w + 2 ( - p - s + f ( v - 2 h ) ) z ) 2 4 ( - p - s + f ( v - 2 h ) ) ( - 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 ) ) ) / ( ( - p - s + f ( v - 2 h ) ) 2 - ( - 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 ) ( ( a + c ( v - 2 h ) - w ) ( a + c ( v - 2 h ) - w + 2 ( p - s + f ( v - 2 h ) ) z ) Γ ( 1 2 , - ( a + c ( v - 2 h ) - w + 2 ( p - s + f ( v - 2 h ) ) z ) 2 4 ( p - s + f ( v - 2 h ) ) ) + 2 ( a + c ( v - 2 h ) - w + 2 ( p - s + f ( v - 2 h ) ) z ) 2 4 ( p - s + f ( v - 2 h ) ) ( 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 ) ) ) / ( ( p - s + f ( v - 2 h ) ) 2 - ( 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 ) ( ( - a + c ( v - 2 h ) + w ) ( - a + c ( v - 2 h ) + w + 2 ( - p + s + f ( v - 2 h ) ) z ) Γ ( 1 2 , - ( - a + c ( v - 2 h ) + w + 2 ( - p + s + f ( v - 2 h ) ) z ) 2 4 ( - p + s + f ( v - 2 h ) ) ) + 2 ( - a + c ( v - 2 h ) + w + 2 ( - p + s + f ( v - 2 h ) ) z ) 2 4 ( - p + s + f ( v - 2 h ) ) ( - 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 ) ) ) / ( ( - p + s + f ( v - 2 h ) ) 2 - ( - 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 ) ( ( a + c ( v - 2 h ) + w ) ( a + c ( v - 2 h ) + w + 2 ( p + s + f ( v - 2 h ) ) z ) Γ ( 1 2 , - ( a + c ( v - 2 h ) + w + 2 ( p + s + f ( v - 2 h ) ) z ) 2 4 ( p + s + f ( v - 2 h ) ) ) + 2 ( a + c ( v - 2 h ) + w + 2 ( p + s + f ( v - 2 h ) ) z ) 2 4 ( p + s + f ( v - 2 h ) ) ( 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 ) ) ) / ( ( p + s + f ( v - 2 h ) ) 2 - ( a + c ( v - 2 h ) + w + 2 ( p + s + f ( v - 2 h ) ) z ) 2 p + s + f ( v - 2 h ) ) ) /; v TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] v > 0 Condition z z 1 2 a q p z t s z w z 1 2 z 1 2 c g f z v 2 -1 v -3 -1 -1 -1 a -1 w 2 4 -1 p -1 s -1 -1 q -1 t 2 -1 a -1 w 2 -1 p -1 s z 1 2 2 4 -1 p -1 s -1 -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 -1 a -1 w -1 a -1 w 2 -1 p -1 s z 1 2 Gamma 1 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 -1 -1 a -1 w 2 -1 p -1 s z 1 2 2 -1 p -1 s -1 1 2 -1 -1 a -1 w 2 4 p -1 s -1 q -1 t 2 a -1 w 2 p -1 s z 1 2 2 4 p -1 s -1 -1 a -1 w 2 p -1 s z 1 2 2 p -1 s -1 1 2 p -1 s a -1 w a -1 w 2 p -1 s z 1 2 Gamma 1 2 -1 a -1 w 2 p -1 s z 1 2 2 4 p -1 s -1 p -1 s 2 -1 a -1 w 2 p -1 s z 1 2 2 p -1 s -1 1 2 -1 -1 -1 a w 2 4 s -1 p -1 -1 q t 2 -1 a w 2 s -1 p z 1 2 2 4 s -1 p -1 -1 -1 a w 2 s -1 p z 1 2 2 s -1 p -1 1 2 s -1 p -1 a w -1 a w 2 s -1 p z 1 2 Gamma 1 2 -1 -1 a w 2 s -1 p z 1 2 2 4 s -1 p -1 s -1 p 2 -1 -1 a w 2 s -1 p z 1 2 2 s -1 p -1 1 2 -1 -1 -1 a w 2 4 p s -1 q t 2 a w 2 p s z 1 2 2 4 p s -1 -1 a w 2 p s z 1 2 2 p s -1 1 2 p s a w a w 2 p s z 1 2 Gamma 1 2 -1 a w 2 p s z 1 2 2 4 p s -1 p s 2 -1 a w 2 p s z 1 2 2 p s -1 1 2 -1 Binomial v v 2 -1 1 -1 \$CellContext`v 2 2 -1 v -3 h 0 v -1 2 -1 Binomial v h -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 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 -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 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 p -1 s f 2 h -1 v -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 p -1 s f 2 h -1 v 2 -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 -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 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 -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 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 p s f 2 h -1 v -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 p s f 2 h -1 v 2 -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 -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 -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 -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 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 p -1 s f 2 h -1 v -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 -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 -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 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 -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 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 p s f 2 h -1 v -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 p s f 2 h -1 v 2 -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 -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 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 -1 -1 a c v -1 2 h 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z 1 2 2 4 -1 p s f v -1 2 h -1 2 -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 p s f v -1 2 h -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 p s f v -1 2 h 2 -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 -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 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 -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 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 p s f v -1 2 h -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 p s f v -1 2 h 2 -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 v v 0 [/itex]

 Rule Form

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

 2002-12-18