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 Exp

 http://functions.wolfram.com/01.03.21.0594.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18