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 Exp

 http://functions.wolfram.com/01.03.21.0578.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18