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 Exp

 http://functions.wolfram.com/01.03.21.0601.01

 Input Form

 Integrate[z^n a^(b z^2 + d z) h^(c z^2 + f z), z] == ((-(1/2)) (b Log[a] + c Log[h])^(-1 - n) Sum[2^(j - n) Binomial[n, j] Gamma[(1 + j)/2, -(((d + 2 b z) Log[a] + (f + 2 c z) Log[h])^2/ (4 (b Log[a] + c Log[h])))] ((-d) Log[a] - f Log[h])^(-j + n) ((d + 2 b z) Log[a] + (f + 2 c z) Log[h])^(1 + j) (-(((d + 2 b z) Log[a] + (f + 2 c z) Log[h])^2/(b Log[a] + c Log[h])))^ ((1/2) (-1 - j)), {j, 0, n}])/ E^((d Log[a] + f Log[h])^2/(4 (b Log[a] + c Log[h]))) /; Element[n, Integers] && n >= 0

 Standard Form

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 MathML Form

 z n a b z 2 + d z h c z 2 + f z z - 1 2 - ( d log ( a ) + f log ( h ) ) 2 4 ( b log ( a ) + c log ( h ) ) ( b log ( a ) + c log ( h ) ) - n - 1 j = 0 n 2 j - n ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["j", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] Γ ( j + 1 2 , - ( ( d + 2 b z ) log ( a ) + ( f + 2 c z ) log ( h ) ) 2 4 ( b log ( a ) + c log ( h ) ) ) ( - d log ( a ) - f log ( h ) ) n - j ( ( d + 2 b z ) log ( a ) + ( f + 2 c z ) log ( h ) ) j + 1 ( - ( ( d + 2 b z ) log ( a ) + ( f + 2 c z ) log ( h ) ) 2 b log ( a ) + c log ( h ) ) 1 2 ( - j - 1 ) /; n Condition z z n a b z 2 d z h c z 2 f z -1 1 2 -1 d a f h 2 4 b a c h -1 b a c h -1 n -1 j 0 n 2 j -1 n Binomial n j Gamma j 1 2 -1 -1 d 2 b z a f 2 c z h 2 4 b a c h -1 -1 d a -1 f h n -1 j d 2 b z a f 2 c z h j 1 -1 d 2 b z a f 2 c z h 2 b a c h -1 1 2 -1 j -1 n [/itex]

 Rule Form

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

 2002-12-18

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