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/01.20.21.4862.01

 Input Form

 Integrate[E^(b Sqrt[z] + d z + e) 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^(e - I q - t - ((-I) a + b - w)^2/(4 (d - I p - s)))) (2 E^(((-I) a + b - w + 2 (d - I p - s) Sqrt[z])^2/(4 (d - I p - s))) (d - I p - s) Sqrt[-(((-I) a + b - w + 2 (d - I p - s) Sqrt[z])^2/ (d - I p - s))] + ((-I) a + b - w) ((-I) a + b - w + 2 (d - I p - s) Sqrt[z]) Gamma[1/2, -(((-I) a + b - w + 2 (d - I p - s) Sqrt[z])^2/ (4 (d - I p - s)))]))/((d - I p - s)^2 Sqrt[-(((-I) a + b - w + 2 (d - I p - s) Sqrt[z])^2/(d - I p - s))]) + (E^(e + I q - t - (I a + b - w)^2/(4 (d + I p - s))) (2 E^((I a + b - w + 2 (d + I p - s) Sqrt[z])^2/(4 (d + I p - s))) (d + I p - s) Sqrt[-((I a + b - w + 2 (d + I p - s) Sqrt[z])^2/ (d + I p - s))] + (I a + b - w) (I a + b - w + 2 (d + I p - s) Sqrt[z]) Gamma[1/2, -((I a + b - w + 2 (d + I p - s) Sqrt[z])^2/(4 (d + I p - s)))]))/ ((d + I p - s)^2 Sqrt[-((I a + b - w + 2 (d + I p - s) Sqrt[z])^2/ (d + I p - s))]) + (E^(e - I q + t - ((-I) a + b + w)^2/(4 (d - I p + s))) (2 E^(((-I) a + b + w + 2 (d - I p + s) Sqrt[z])^2/(4 (d - I p + s))) (d - I p + s) Sqrt[-(((-I) a + b + w + 2 (d - I p + s) Sqrt[z])^2/ (d - I p + s))] + ((-I) a + b + w) ((-I) a + b + w + 2 (d - I p + s) Sqrt[z]) Gamma[1/2, -(((-I) a + b + w + 2 (d - I p + s) Sqrt[z])^2/ (4 (d - I p + s)))]))/((d - I p + s)^2 Sqrt[-(((-I) a + b + w + 2 (d - I p + s) Sqrt[z])^2/(d - I p + s))]) + ((-E^(e + I q + t - (I a + b + w)^2/(4 (d + I p + s)))) (2 E^((I a + b + w + 2 (d + I p + s) Sqrt[z])^2/(4 (d + I p + s))) (d + I p + s) Sqrt[-((I a + b + w + 2 (d + I p + s) Sqrt[z])^2/ (d + I p + s))] + (I a + b + w) (I a + b + w + 2 (d + I p + s) Sqrt[z]) Gamma[1/2, -((I a + b + w + 2 (d + I p + s) Sqrt[z])^2/(4 (d + I p + s)))]))/ ((d + I p + s)^2 Sqrt[-((I a + b + w + 2 (d + I p + s) Sqrt[z])^2/ (d + I p + s))])) (1 - Mod[v, 2]) + I 2^(-3 - v) Sum[Binomial[v, h] (((-E^(e - I q - t + g (2 h - v) - ((-I) a + b + c (2 h - v) - w)^2/ (4 (d - I p - s + f (2 h - v))))) (2 E^(((-I) a + b + c (2 h - v) - w + 2 (d - I p - s + f (2 h - v)) Sqrt[z])^2/(4 (d - I p - s + f (2 h - v)))) (d - I p - s + f (2 h - v)) Sqrt[-(((-I) a + b + c (2 h - v) - w + 2 (d - I p - s + f (2 h - v)) Sqrt[z])^2/(d - I p - s + f (2 h - v)))] + ((-I) a + b + c (2 h - v) - w) ((-I) a + b + c (2 h - v) - w + 2 (d - I p - s + f (2 h - v)) Sqrt[z]) Gamma[1/2, -(((-I) a + b + c (2 h - v) - w + 2 (d - I p - s + f (2 h - v)) Sqrt[z])^2/(4 (d - I p - s + f (2 h - v))))]))/((d - I p - s + f (2 h - v))^2 Sqrt[-(((-I) a + b + c (2 h - v) - w + 2 (d - I p - s + f (2 h - v)) Sqrt[z])^2/(d - I p - s + f (2 h - v)))]) + (E^(e + I q - t + g (2 h - v) - (I a + b + c (2 h - v) - w)^2/ (4 (d + I p - s + f (2 h - v)))) (2 E^((I a + b + c (2 h - v) - w + 2 (d + I p - s + f (2 h - v)) Sqrt[z])^2/(4 (d + I p - s + f (2 h - v)))) (d + I p - s + f (2 h - v)) Sqrt[-((I a + b + c (2 h - v) - w + 2 (d + I p - s + f (2 h - v)) Sqrt[z])^2/(d + I p - s + f (2 h - v)))] + (I a + b + c (2 h - v) - w) (I a + b + c (2 h - v) - w + 2 (d + I p - s + f (2 h - v)) Sqrt[z]) Gamma[1/2, -((I a + b + c (2 h - v) - w + 2 (d + I p - s + f (2 h - v)) Sqrt[z])^2/(4 (d + I p - s + f (2 h - v))))]))/((d + I p - s + f (2 h - v))^2 Sqrt[-((I a + b + c (2 h - v) - w + 2 (d + I p - s + f (2 h - v)) Sqrt[z])^2/(d + I p - s + f (2 h - v)))]) + (E^(e - I q + t + g (2 h - v) - ((-I) a + b + c (2 h - v) + w)^2/ (4 (d - I p + s + f (2 h - v)))) (2 E^(((-I) a + b + c (2 h - v) + w + 2 (d - I p + s + f (2 h - v)) Sqrt[z])^2/(4 (d - I p + s + f (2 h - v)))) (d - I p + s + f (2 h - v)) Sqrt[-(((-I) a + b + c (2 h - v) + w + 2 (d - I p + s + f (2 h - v)) Sqrt[z])^2/(d - I p + s + f (2 h - v)))] + ((-I) a + b + c (2 h - v) + w) ((-I) a + b + c (2 h - v) + w + 2 (d - I p + s + f (2 h - v)) Sqrt[z]) Gamma[1/2, -(((-I) a + b + c (2 h - v) + w + 2 (d - I p + s + f (2 h - v)) Sqrt[z])^2/(4 (d - I p + s + f (2 h - v))))]))/((d - I p + s + f (2 h - v))^2 Sqrt[-(((-I) a + b + c (2 h - v) + w + 2 (d - I p + s + f (2 h - v)) Sqrt[z])^2/(d - I p + s + f (2 h - v)))]) + ((-E^(e + I q + t + g (2 h - v) - (I a + b + c (2 h - v) + w)^2/ (4 (d + I p + s + f (2 h - v))))) (2 E^((I a + b + c (2 h - v) + w + 2 (d + I p + s + f (2 h - v)) Sqrt[z])^2/(4 (d + I p + s + f (2 h - v)))) (d + I p + s + f (2 h - v)) Sqrt[-((I a + b + c (2 h - v) + w + 2 (d + I p + s + f (2 h - v)) Sqrt[z])^2/(d + I p + s + f (2 h - v)))] + (I a + b + c (2 h - v) + w) (I a + b + c (2 h - v) + w + 2 (d + I p + s + f (2 h - v)) Sqrt[z]) Gamma[1/2, -((I a + b + c (2 h - v) + w + 2 (d + I p + s + f (2 h - v)) Sqrt[z])^2/(4 (d + I p + s + f (2 h - v))))]))/((d + I p + s + f (2 h - v))^2 Sqrt[-((I a + b + c (2 h - v) + w + 2 (d + I p + s + f (2 h - v)) Sqrt[z])^2/(d + I p + s + f (2 h - v)))]) + ((-E^(e - I q - t + g (-2 h + v) - ((-I) a + b + c (-2 h + v) - w)^2/ (4 (d - I p - s + f (-2 h + v))))) (2 E^(((-I) a + b + c (-2 h + v) - w + 2 (d - I p - s + f (-2 h + v)) Sqrt[z])^2/(4 (d - I p - s + f (-2 h + v)))) (d - I p - s + f (-2 h + v)) Sqrt[-(((-I) a + b + c (-2 h + v) - w + 2 (d - I p - s + f (-2 h + v)) Sqrt[z])^2/ (d - I p - s + f (-2 h + v)))] + ((-I) a + b + c (-2 h + v) - w) ((-I) a + b + c (-2 h + v) - w + 2 (d - I p - s + f (-2 h + v)) Sqrt[z]) Gamma[1/2, -(((-I) a + b + c (-2 h + v) - w + 2 (d - I p - s + f (-2 h + v)) Sqrt[z])^2/(4 (d - I p - s + f (-2 h + v))))]))/ ((d - I p - s + f (-2 h + v))^2 Sqrt[-(((-I) a + b + c (-2 h + v) - w + 2 (d - I p - s + f (-2 h + v)) Sqrt[z])^2/(d - I p - s + f (-2 h + v)))]) + (E^(e + I q - t + g (-2 h + v) - (I a + b + c (-2 h + v) - w)^2/ (4 (d + I p - s + f (-2 h + v)))) (2 E^((I a + b + c (-2 h + v) - w + 2 (d + I p - s + f (-2 h + v)) Sqrt[z])^2/(4 (d + I p - s + f (-2 h + v)))) (d + I p - s + f (-2 h + v)) Sqrt[-((I a + b + c (-2 h + v) - w + 2 (d + I p - s + f (-2 h + v)) Sqrt[z])^2/(d + I p - s + f (-2 h + v)))] + (I a + b + c (-2 h + v) - w) (I a + b + c (-2 h + v) - w + 2 (d + I p - s + f (-2 h + v)) Sqrt[z]) Gamma[1/2, -((I a + b + c (-2 h + v) - w + 2 (d + I p - s + f (-2 h + v)) Sqrt[z])^2/(4 (d + I p - s + f (-2 h + v))))]))/((d + I p - s + f (-2 h + v))^2 Sqrt[-((I a + b + c (-2 h + v) - w + 2 (d + I p - s + f (-2 h + v)) Sqrt[z])^2/(d + I p - s + f (-2 h + v)))]) + (E^(e - I q + t + g (-2 h + v) - ((-I) a + b + c (-2 h + v) + w)^2/ (4 (d - I p + s + f (-2 h + v)))) (2 E^(((-I) a + b + c (-2 h + v) + w + 2 (d - I p + s + f (-2 h + v)) Sqrt[z])^2/(4 (d - I p + s + f (-2 h + v)))) (d - I p + s + f (-2 h + v)) Sqrt[-(((-I) a + b + c (-2 h + v) + w + 2 (d - I p + s + f (-2 h + v)) Sqrt[z])^2/ (d - I p + s + f (-2 h + v)))] + ((-I) a + b + c (-2 h + v) + w) ((-I) a + b + c (-2 h + v) + w + 2 (d - I p + s + f (-2 h + v)) Sqrt[z]) Gamma[1/2, -(((-I) a + b + c (-2 h + v) + w + 2 (d - I p + s + f (-2 h + v)) Sqrt[z])^2/(4 (d - I p + s + f (-2 h + v))))]))/ ((d - I p + s + f (-2 h + v))^2 Sqrt[-(((-I) a + b + c (-2 h + v) + w + 2 (d - I p + s + f (-2 h + v)) Sqrt[z])^2/(d - I p + s + f (-2 h + v)))]) + ((-E^(e + I q + t + g (-2 h + v) - (I a + b + c (-2 h + v) + w)^2/ (4 (d + I p + s + f (-2 h + v))))) (2 E^((I a + b + c (-2 h + v) + w + 2 (d + I p + s + f (-2 h + v)) Sqrt[z])^2/(4 (d + I p + s + f (-2 h + v)))) (d + I p + s + f (-2 h + v)) Sqrt[-((I a + b + c (-2 h + v) + w + 2 (d + I p + s + f (-2 h + v)) Sqrt[z])^2/(d + I p + s + f (-2 h + v)))] + (I a + b + c (-2 h + v) + w) (I a + b + c (-2 h + v) + w + 2 (d + I p + s + f (-2 h + v)) Sqrt[z]) Gamma[1/2, -((I a + b + c (-2 h + v) + w + 2 (d + I p + s + f (-2 h + v)) Sqrt[z])^2/(4 (d + I p + s + f (-2 h + v))))]))/((d + I p + s + f (-2 h + v))^2 Sqrt[-((I a + b + c (-2 h + v) + w + 2 (d + I p + s + f (-2 h + v)) Sqrt[z])^2/(d + 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

 z b + e + d z sin ( z a + q + p z ) sinh ( t + s z + w z ) cosh v ( z c + g + f z ) z 2 - v - 3 ( ( - ( b + a - w ) 2 4 ( d + p - s ) + e + q - t ( 2 ( b + a - w + 2 ( d + p - s ) z ) 2 4 ( d + p - s ) - ( b + a - w + 2 ( d + p - s ) z ) 2 d + p - s ( d + p - s ) + ( b + a - w ) ( b + a - w + 2 ( d + p - s ) z ) Γ ( 1 2 , - ( b + a - w + 2 ( d + p - s ) z ) 2 4 ( d + p - s ) ) ) ) / ( ( d + p - s ) 2 - ( b + a - w + 2 ( d + p - s ) z ) 2 d + p - s ) - ( - ( b + - a - w ) 2 4 ( d - p - s ) + e - q - t ( 2 ( b + - a - w + 2 ( d - p - s ) z ) 2 4 ( d - p - s ) - ( b + - a - w + 2 ( d - p - s ) z ) 2 d - p - s ( d - p - s ) + ( b + - a - w ) ( b + - a - w + 2 ( d - p - s ) z ) Γ ( 1 2 , - ( b + - a - w + 2 ( d - p - s ) z ) 2 4 ( d - p - s ) ) ) ) / ( ( d - p - s ) 2 - ( b + - a - w + 2 ( d - p - s ) z ) 2 d - p - s ) + - ( - ( b + a + w ) 2 4 ( d + p + s ) + e + q + t ( 2 ( b + a + w + 2 ( d + p + s ) z ) 2 4 ( d + p + s ) - ( b + a + w + 2 ( d + p + s ) z ) 2 d + p + s ( d + p + s ) + ( b + a + w ) ( b + a + w + 2 ( d + p + s ) z ) Γ ( 1 2 , - ( b + a + w + 2 ( d + p + s ) z ) 2 4 ( d + p + s ) ) ) ) / ( ( d + p + s ) 2 - ( b + a + w + 2 ( d + p + s ) z ) 2 d + p + s ) + ( - ( b + - a + w ) 2 4 ( d - p + s ) + e - q + t ( 2 ( b + - a + w + 2 ( d - p + s ) z ) 2 4 ( d - p + s ) - ( b + - a + w + 2 ( d - p + s ) z ) 2 d - p + s ( d - p + s ) + ( b + - a + w ) ( b + - a + w + 2 ( d - p + s ) z ) Γ ( 1 2 , - ( b + - a + w + 2 ( d - p + s ) z ) 2 4 ( d - p + s ) ) ) ) / ( ( d - p + s ) 2 - ( b + - a + w + 2 ( d - p + s ) z ) 2 d - 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]] ( ( - ( b + a + c ( 2 h - v ) - w ) 2 4 ( d + p - s + f ( 2 h - v ) ) + e + q - t + g ( 2 h - v ) ( ( b + a + c ( 2 h - v ) - w ) ( b + a + c ( 2 h - v ) - w + 2 ( d + p - s + f ( 2 h - v ) ) z ) Γ ( 1 2 , - ( b + a + c ( 2 h - v ) - w + 2 ( d + p - s + f ( 2 h - v ) ) z ) 2 4 ( d + p - s + f ( 2 h - v ) ) ) + 2 ( b + a + c ( 2 h - v ) - w + 2 ( d + p - s + f ( 2 h - v ) ) z ) 2 4 ( d + p - s + f ( 2 h - v ) ) ( d + p - s + f ( 2 h - v ) ) - ( b + a + c ( 2 h - v ) - w + 2 ( d + p - s + f ( 2 h - v ) ) z ) 2 d + p - s + f ( 2 h - v ) ) ) / ( ( d + p - s + f ( 2 h - v ) ) 2 - ( b + a + c ( 2 h - v ) - w + 2 ( d + p - s + f ( 2 h - v ) ) z ) 2 d + p - s + f ( 2 h - v ) ) - ( - ( b - a + c ( 2 h - v ) - w ) 2 4 ( d - p - s + f ( 2 h - v ) ) + e - q - t + g ( 2 h - v ) ( ( b - a + c ( 2 h - v ) - w ) ( b - a + c ( 2 h - v ) - w + 2 ( d - p - s + f ( 2 h - v ) ) z ) Γ ( 1 2 , - ( b - a + c ( 2 h - v ) - w + 2 ( d - p - s + f ( 2 h - v ) ) z ) 2 4 ( d - p - s + f ( 2 h - v ) ) ) + 2 ( b - a + c ( 2 h - v ) - w + 2 ( d - p - s + f ( 2 h - v ) ) z ) 2 4 ( d - p - s + f ( 2 h - v ) ) ( d - p - s + f ( 2 h - v ) ) - ( b - a + c ( 2 h - v ) - w + 2 ( d - p - s + f ( 2 h - v ) ) z ) 2 d - p - s + f ( 2 h - v ) ) ) / ( ( d - p - s + f ( 2 h - v ) ) 2 - ( b - a + c ( 2 h - v ) - w + 2 ( d - p - s + f ( 2 h - v ) ) z ) 2 d - p - s + f ( 2 h - v ) ) - ( - ( b + a + c ( 2 h - v ) + w ) 2 4 ( d + p + s + f ( 2 h - v ) ) + e + q + t + g ( 2 h - v ) ( ( b + a + c ( 2 h - v ) + w ) ( b + a + c ( 2 h - v ) + w + 2 ( d + p + s + f ( 2 h - v ) ) z ) Γ ( 1 2 , - ( b + a + c ( 2 h - v ) + w + 2 ( d + p + s + f ( 2 h - v ) ) z ) 2 4 ( d + p + s + f ( 2 h - v ) ) ) + 2 ( b + a + c ( 2 h - v ) + w + 2 ( d + p + s + f ( 2 h - v ) ) z ) 2 4 ( d + p + s + f ( 2 h - v ) ) ( d + p + s + f ( 2 h - v ) ) - ( b + a + c ( 2 h - v ) + w + 2 ( d + p + s + f ( 2 h - v ) ) z ) 2 d + p + s + f ( 2 h - v ) ) ) / ( ( d + p + s + f ( 2 h - v ) ) 2 - ( b + a + c ( 2 h - v ) + w + 2 ( d + p + s + f ( 2 h - v ) ) z ) 2 d + p + s + f ( 2 h - v ) ) + ( - ( b - a + c ( 2 h - v ) + w ) 2 4 ( d - p + s + f ( 2 h - v ) ) + e - q + t + g ( 2 h - v ) ( ( b - a + c ( 2 h - v ) + w ) ( b - a + c ( 2 h - v ) + w + 2 ( d - p + s + f ( 2 h - v ) ) z ) Γ ( 1 2 , - ( b - a + c ( 2 h - v ) + w + 2 ( d - p + s + f ( 2 h - v ) ) z ) 2 4 ( d - p + s + f ( 2 h - v ) ) ) + 2 ( b - a + c ( 2 h - v ) + w + 2 ( d - p + s + f ( 2 h - v ) ) z ) 2 4 ( d - p + s + f ( 2 h - v ) ) ( d - p + s + f ( 2 h - v ) ) - ( b - a + c ( 2 h - v ) + w + 2 ( d - p + s + f ( 2 h - v ) ) z ) 2 d - p + s + f ( 2 h - v ) ) ) / ( ( d - p + s + f ( 2 h - v ) ) 2 - ( b - a + c ( 2 h - v ) + w + 2 ( d - p + s + f ( 2 h - v ) ) z ) 2 d - p + s + f ( 2 h - v ) ) + ( - ( b + a + c ( v - 2 h ) - w ) 2 4 ( d + p - s + f ( v - 2 h ) ) + e + q - t + g ( v - 2 h ) ( ( b + a + c ( v - 2 h ) - w ) ( b + a + c ( v - 2 h ) - w + 2 ( d + p - s + f ( v - 2 h ) ) z ) Γ ( 1 2 , - ( b + a + c ( v - 2 h ) - w + 2 ( d + p - s + f ( v - 2 h ) ) z ) 2 4 ( d + p - s + f ( v - 2 h ) ) ) + 2 ( b + a + c ( v - 2 h ) - w + 2 ( d + p - s + f ( v - 2 h ) ) z ) 2 4 ( d + p - s + f ( v - 2 h ) ) ( d + p - s + f ( v - 2 h ) ) - ( b + a + c ( v - 2 h ) - w + 2 ( d + p - s + f ( v - 2 h ) ) z ) 2 d + p - s + f ( v - 2 h ) ) ) / ( ( d + p - s + f ( v - 2 h ) ) 2 - ( b + a + c ( v - 2 h ) - w + 2 ( d + p - s + f ( v - 2 h ) ) z ) 2 d + p - s + f ( v - 2 h ) ) - ( - ( b - a + c ( v - 2 h ) - w ) 2 4 ( d - p - s + f ( v - 2 h ) ) + e - q - t + g ( v - 2 h ) ( ( b - a + c ( v - 2 h ) - w ) ( b - a + c ( v - 2 h ) - w + 2 ( d - p - s + f ( v - 2 h ) ) z ) Γ ( 1 2 , - ( b - a + c ( v - 2 h ) - w + 2 ( d - p - s + f ( v - 2 h ) ) z ) 2 4 ( d - p - s + f ( v - 2 h ) ) ) + 2 ( b - a + c ( v - 2 h ) - w + 2 ( d - p - s + f ( v - 2 h ) ) z ) 2 4 ( d - p - s + f ( v - 2 h ) ) ( d - p - s + f ( v - 2 h ) ) - ( b - a + c ( v - 2 h ) - w + 2 ( d - p - s + f ( v - 2 h ) ) z ) 2 d - p - s + f ( v - 2 h ) ) ) / ( ( d - p - s + f ( v - 2 h ) ) 2 - ( b - a + c ( v - 2 h ) - w + 2 ( d - p - s + f ( v - 2 h ) ) z ) 2 d - p - s + f ( v - 2 h ) ) - ( - ( b + a + c ( v - 2 h ) + w ) 2 4 ( d + p + s + f ( v - 2 h ) ) + e + q + t + g ( v - 2 h ) ( ( b + a + c ( v - 2 h ) + w ) ( b + a + c ( v - 2 h ) + w + 2 ( d + p + s + f ( v - 2 h ) ) z ) Γ ( 1 2 , - ( b + a + c ( v - 2 h ) + w + 2 ( d + p + s + f ( v - 2 h ) ) z ) 2 4 ( d + p + s + f ( v - 2 h ) ) ) + 2 ( b + a + c ( v - 2 h ) + w + 2 ( d + p + s + f ( v - 2 h ) ) z ) 2 4 ( d + p + s + f ( v - 2 h ) ) ( d + p + s + f ( v - 2 h ) ) - ( b + a + c ( v - 2 h ) + w + 2 ( d + p + s + f ( v - 2 h ) ) z ) 2 d + p + s + f ( v - 2 h ) ) ) / ( ( d + p + s + f ( v - 2 h ) ) 2 - ( b + a + c ( v - 2 h ) + w + 2 ( d + p + s + f ( v - 2 h ) ) z ) 2 d + p + s + f ( v - 2 h ) ) + ( - ( b - a + c ( v - 2 h ) + w ) 2 4 ( d - p + s + f ( v - 2 h ) ) + e - q + t + g ( v - 2 h ) ( ( b - a + c ( v - 2 h ) + w ) ( b - a + c ( v - 2 h ) + w + 2 ( d - p + s + f ( v - 2 h ) ) z ) Γ ( 1 2 , - ( b - a + c ( v - 2 h ) + w + 2 ( d - p + s + f ( v - 2 h ) ) z ) 2 4 ( d - p + s + f ( v - 2 h ) ) ) + 2 ( b - a + c ( v - 2 h ) + w + 2 ( d - p + s + f ( v - 2 h ) ) z ) 2 4 ( d - p + s + f ( v - 2 h ) ) ( d - p + s + f ( v - 2 h ) ) - ( b - a + c ( v - 2 h ) + w + 2 ( d - p + s + f ( v - 2 h ) ) z ) 2 d - p + s + f ( v - 2 h ) ) ) / ( ( d - p + s + f ( v - 2 h ) ) 2 - ( b - a + c ( v - 2 h ) + w + 2 ( d - p + s + f ( v - 2 h ) ) z ) 2 d - p + s + f ( v - 2 h ) ) ) /; v + Condition z z 1 2 b e d 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 b a -1 w 2 4 d p -1 s -1 e q -1 t 2 b a -1 w 2 d p -1 s z 1 2 2 4 d p -1 s -1 -1 b a -1 w 2 d p -1 s z 1 2 2 d p -1 s -1 1 2 d p -1 s b a -1 w b a -1 w 2 d p -1 s z 1 2 Gamma 1 2 -1 b a -1 w 2 d p -1 s z 1 2 2 4 d p -1 s -1 d p -1 s 2 -1 b a -1 w 2 d p -1 s z 1 2 2 d p -1 s -1 1 2 -1 -1 -1 b -1 a -1 w 2 4 d -1 p -1 s -1 e -1 q -1 t 2 b -1 a -1 w 2 d -1 p -1 s z 1 2 2 4 d -1 p -1 s -1 -1 b -1 a -1 w 2 d -1 p -1 s z 1 2 2 d -1 p -1 s -1 1 2 d -1 p -1 s b -1 a -1 w b -1 a -1 w 2 d -1 p -1 s z 1 2 Gamma 1 2 -1 b -1 a -1 w 2 d -1 p -1 s z 1 2 2 4 d -1 p -1 s -1 d -1 p -1 s 2 -1 b -1 a -1 w 2 d -1 p -1 s z 1 2 2 d -1 p -1 s -1 1 2 -1 -1 -1 b a w 2 4 d p s -1 e q t 2 b a w 2 d p s z 1 2 2 4 d p s -1 -1 b a w 2 d p s z 1 2 2 d p s -1 1 2 d p s b a w b a w 2 d p s z 1 2 Gamma 1 2 -1 b a w 2 d p s z 1 2 2 4 d p s -1 d p s 2 -1 b a w 2 d p s z 1 2 2 d p s -1 1 2 -1 -1 b -1 a w 2 4 d -1 p s -1 e -1 q t 2 b -1 a w 2 d -1 p s z 1 2 2 4 d -1 p s -1 -1 b -1 a w 2 d -1 p s z 1 2 2 d -1 p s -1 1 2 d -1 p s b -1 a w b -1 a w 2 d -1 p s z 1 2 Gamma 1 2 -1 b -1 a w 2 d -1 p s z 1 2 2 4 d -1 p s -1 d -1 p s 2 -1 b -1 a w 2 d -1 p s z 1 2 2 d -1 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 b a c 2 h -1 v -1 w 2 4 d p -1 s f 2 h -1 v -1 e q -1 t g 2 h -1 v b a c 2 h -1 v -1 w b a c 2 h -1 v -1 w 2 d p -1 s f 2 h -1 v z 1 2 Gamma 1 2 -1 b a c 2 h -1 v -1 w 2 d p -1 s f 2 h -1 v z 1 2 2 4 d p -1 s f 2 h -1 v -1 2 b a c 2 h -1 v -1 w 2 d p -1 s f 2 h -1 v z 1 2 2 4 d p -1 s f 2 h -1 v -1 d p -1 s f 2 h -1 v -1 b a c 2 h -1 v -1 w 2 d p -1 s f 2 h -1 v z 1 2 2 d p -1 s f 2 h -1 v -1 1 2 d p -1 s f 2 h -1 v 2 -1 b a c 2 h -1 v -1 w 2 d p -1 s f 2 h -1 v z 1 2 2 d p -1 s f 2 h -1 v -1 1 2 -1 -1 -1 b -1 a c 2 h -1 v -1 w 2 4 d -1 p -1 s f 2 h -1 v -1 e -1 q -1 t g 2 h -1 v b -1 a c 2 h -1 v -1 w b -1 a c 2 h -1 v -1 w 2 d -1 p -1 s f 2 h -1 v z 1 2 Gamma 1 2 -1 b -1 a c 2 h -1 v -1 w 2 d -1 p -1 s f 2 h -1 v z 1 2 2 4 d -1 p -1 s f 2 h -1 v -1 2 b -1 a c 2 h -1 v -1 w 2 d -1 p -1 s f 2 h -1 v z 1 2 2 4 d -1 p -1 s f 2 h -1 v -1 d -1 p -1 s f 2 h -1 v -1 b -1 a c 2 h -1 v -1 w 2 d -1 p -1 s f 2 h -1 v z 1 2 2 d -1 p -1 s f 2 h -1 v -1 1 2 d -1 p -1 s f 2 h -1 v 2 -1 b -1 a c 2 h -1 v -1 w 2 d -1 p -1 s f 2 h -1 v z 1 2 2 d -1 p -1 s f 2 h -1 v -1 1 2 -1 -1 -1 b a c 2 h -1 v w 2 4 d p s f 2 h -1 v -1 e q t g 2 h -1 v b a c 2 h -1 v w b a c 2 h -1 v w 2 d p s f 2 h -1 v z 1 2 Gamma 1 2 -1 b a c 2 h -1 v w 2 d p s f 2 h -1 v z 1 2 2 4 d p s f 2 h -1 v -1 2 b a c 2 h -1 v w 2 d p s f 2 h -1 v z 1 2 2 4 d p s f 2 h -1 v -1 d p s f 2 h -1 v -1 b a c 2 h -1 v w 2 d p s f 2 h -1 v z 1 2 2 d p s f 2 h -1 v -1 1 2 d p s f 2 h -1 v 2 -1 b a c 2 h -1 v w 2 d p s f 2 h -1 v z 1 2 2 d p s f 2 h -1 v -1 1 2 -1 -1 b -1 a c 2 h -1 v w 2 4 d -1 p s f 2 h -1 v -1 e -1 q t g 2 h -1 v b -1 a c 2 h -1 v w b -1 a c 2 h -1 v w 2 d -1 p s f 2 h -1 v z 1 2 Gamma 1 2 -1 b -1 a c 2 h -1 v w 2 d -1 p s f 2 h -1 v z 1 2 2 4 d -1 p s f 2 h -1 v -1 2 b -1 a c 2 h -1 v w 2 d -1 p s f 2 h -1 v z 1 2 2 4 d -1 p s f 2 h -1 v -1 d -1 p s f 2 h -1 v -1 b -1 a c 2 h -1 v w 2 d -1 p s f 2 h -1 v z 1 2 2 d -1 p s f 2 h -1 v -1 1 2 d -1 p s f 2 h -1 v 2 -1 b -1 a c 2 h -1 v w 2 d -1 p s f 2 h -1 v z 1 2 2 d -1 p s f 2 h -1 v -1 1 2 -1 -1 b a c v -1 2 h -1 w 2 4 d p -1 s f v -1 2 h -1 e q -1 t g v -1 2 h b a c v -1 2 h -1 w b a c v -1 2 h -1 w 2 d p -1 s f v -1 2 h z 1 2 Gamma 1 2 -1 b a c v -1 2 h -1 w 2 d p -1 s f v -1 2 h z 1 2 2 4 d p -1 s f v -1 2 h -1 2 b a c v -1 2 h -1 w 2 d p -1 s f v -1 2 h z 1 2 2 4 d p -1 s f v -1 2 h -1 d p -1 s f v -1 2 h -1 b a c v -1 2 h -1 w 2 d p -1 s f v -1 2 h z 1 2 2 d p -1 s f v -1 2 h -1 1 2 d p -1 s f v -1 2 h 2 -1 b a c v -1 2 h -1 w 2 d p -1 s f v -1 2 h z 1 2 2 d p -1 s f v -1 2 h -1 1 2 -1 -1 -1 b -1 a c v -1 2 h -1 w 2 4 d -1 p -1 s f v -1 2 h -1 e -1 q -1 t g v -1 2 h b -1 a c v -1 2 h -1 w b -1 a c v -1 2 h -1 w 2 d -1 p -1 s f v -1 2 h z 1 2 Gamma 1 2 -1 b -1 a c v -1 2 h -1 w 2 d -1 p -1 s f v -1 2 h z 1 2 2 4 d -1 p -1 s f v -1 2 h -1 2 b -1 a c v -1 2 h -1 w 2 d -1 p -1 s f v -1 2 h z 1 2 2 4 d -1 p -1 s f v -1 2 h -1 d -1 p -1 s f v -1 2 h -1 b -1 a c v -1 2 h -1 w 2 d -1 p -1 s f v -1 2 h z 1 2 2 d -1 p -1 s f v -1 2 h -1 1 2 d -1 p -1 s f v -1 2 h 2 -1 b -1 a c v -1 2 h -1 w 2 d -1 p -1 s f v -1 2 h z 1 2 2 d -1 p -1 s f v -1 2 h -1 1 2 -1 -1 -1 b a c v -1 2 h w 2 4 d p s f v -1 2 h -1 e q t g v -1 2 h b a c v -1 2 h w b a c v -1 2 h w 2 d p s f v -1 2 h z 1 2 Gamma 1 2 -1 b a c v -1 2 h w 2 d p s f v -1 2 h z 1 2 2 4 d p s f v -1 2 h -1 2 b a c v -1 2 h w 2 d p s f v -1 2 h z 1 2 2 4 d p s f v -1 2 h -1 d p s f v -1 2 h -1 b a c v -1 2 h w 2 d p s f v -1 2 h z 1 2 2 d p s f v -1 2 h -1 1 2 d p s f v -1 2 h 2 -1 b a c v -1 2 h w 2 d p s f v -1 2 h z 1 2 2 d p s f v -1 2 h -1 1 2 -1 -1 b -1 a c v -1 2 h w 2 4 d -1 p s f v -1 2 h -1 e -1 q t g v -1 2 h b -1 a c v -1 2 h w b -1 a c v -1 2 h w 2 d -1 p s f v -1 2 h z 1 2 Gamma 1 2 -1 b -1 a c v -1 2 h w 2 d -1 p s f v -1 2 h z 1 2 2 4 d -1 p s f v -1 2 h -1 2 b -1 a c v -1 2 h w 2 d -1 p s f v -1 2 h z 1 2 2 4 d -1 p s f v -1 2 h -1 d -1 p s f v -1 2 h -1 b -1 a c v -1 2 h w 2 d -1 p s f v -1 2 h z 1 2 2 d -1 p s f v -1 2 h -1 1 2 d -1 p s f v -1 2 h 2 -1 b -1 a c v -1 2 h w 2 d -1 p s f v -1 2 h z 1 2 2 d -1 p s f v -1 2 h -1 1 2 -1 v SuperPlus [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b_", " ", SqrtBox["z_"]]], "+", RowBox[List["d_", " ", "z_"]], "+", "e_"]]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["a_", " ", SqrtBox["z_"]]], "+", RowBox[List["p_", " ", "z_"]], "+", "q_"]], "]"]], " ", RowBox[List["Sinh", "[", RowBox[List[RowBox[List["w_", " ", SqrtBox["z_"]]], "+", RowBox[List["s_", " ", "z_"]], "+", "t_"]], "]"]], " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c_", " ", SqrtBox["z_"]]], "+", RowBox[List["f_", " ", "z_"]], "+", "g_"]], "]"]], "v_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "3"]], "-", "v"]]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", 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 Date Added to functions.wolfram.com (modification date)

 2002-12-18