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 Erfc

 http://functions.wolfram.com/06.27.21.0015.01

 Input Form

 Integrate[z^n E^(b z) Erfc[a z], z] == (-(-b)^(-1 - n)) Gamma[1 + n, (-b) z] Erfc[a z] + (-b)^(-1 - n) (a/Sqrt[Pi]) n! E^(b^2/(4 a^2)) Sum[((-b)^m/m!) (-a^2)^((1/2) (-1 - m)) Sum[Binomial[m, k] (-(b/(2 Sqrt[-a^2])))^(m - k) (Sqrt[-a^2] z + b/(2 Sqrt[-a^2]))^(1 + k) (-(Sqrt[-a^2] z + b/(2 Sqrt[-a^2]))^2)^((1/2) (-1 - k)) Gamma[(1 + k)/2, -(Sqrt[-a^2] z + b/(2 Sqrt[-a^2]))^2], {k, 0, m}], {m, 0, n}] /; Element[n, Integers] && n >= 0

 Standard Form

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 MathML Form

 z n b z erfc ( a z ) z a n ! ( - b ) - n - 1 π exp ( b 2 4 a 2 ) m = 0 n ( - b ) m ( - a 2 ) 1 2 ( - m - 1 ) m ! k = 0 m ( 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]] ( - b 2 - a 2 ) m - k ( b 2 - a 2 + - a 2 z ) k + 1 ( - ( b 2 - a 2 + - a 2 z ) 2 ) 1 2 ( - k - 1 ) Γ ( k + 1 2 , - ( b 2 - a 2 + - a 2 z ) 2 ) - ( - b ) - n - 1 erfc ( a z ) Γ ( n + 1 , - b z ) /; n Condition z z n b z Erfc a z a n -1 b -1 n -1 1 2 -1 b 2 4 a 2 -1 m 0 n -1 b m -1 a 2 1 2 -1 m -1 m -1 k 0 m Binomial m k -1 b 2 -1 a 2 1 2 -1 m -1 k b 2 -1 a 2 1 2 -1 -1 a 2 1 2 z k 1 -1 b 2 -1 a 2 1 2 -1 -1 a 2 1 2 z 2 1 2 -1 k -1 Gamma k 1 2 -1 -1 b 2 -1 a 2 1 2 -1 -1 a 2 1 2 z 2 -1 -1 b -1 n -1 Erfc a z Gamma n 1 -1 b z n [/itex]

 Rule Form

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

 2001-10-29