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 Exp

 http://functions.wolfram.com/01.03.21.0561.01

 Input Form

 Integrate[z^n a^(d z) h^(c z + g), z] == h^g z^(1 + n) ((-z) (d Log[a] + c Log[h]))^(-1 - n) (-((1/(2 (-1 - n)!)) ((-1)^n (2 ExpIntegralEi[z (d Log[a] + c Log[h])] + 2 Log[(-z) (d Log[a] + c Log[h])] - Log[z (d Log[a] + c Log[h])] + Log[1/(d z Log[a] + c z Log[h])]))) - a^(d z) h^(c z) Sum[((-z) (d Log[a] + c Log[h]))^k/Pochhammer[1 + n, k - n], {k, 0, n}] + a^(d z) h^(c z) Sum[((-z) (d Log[a] + c Log[h]))^k/ Pochhammer[1 + n, k - n], {k, 1 + n, -1}]) /; Element[n, Integers]

 Standard Form

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 MathML Form

 z n a d z h g + c z z h g z n + 1 ( - z ( d log ( a ) + c log ( h ) ) ) - n - 1 ( - a d z ( k = 0 n ( - z ( d log ( a ) + c log ( h ) ) ) k ( n + 1 ) k - n TagBox[SubscriptBox[RowBox[List["(", RowBox[List["n", "+", "1"]], ")"]], RowBox[List["k", "-", "n"]]], Pochhammer] ) h c z + a d z ( k = n + 1 - 1 ( - z ( d log ( a ) + c log ( h ) ) ) k ( n + 1 ) k - n TagBox[SubscriptBox[RowBox[List["(", RowBox[List["n", "+", "1"]], ")"]], RowBox[List["k", "-", "n"]]], Pochhammer] ) h c z - 1 2 ( - n - 1 ) ! ( - 1 ) n ( 2 Ei ( z ( d log ( a ) + c log ( h ) ) ) + 2 log ( - z ( d log ( a ) + c log ( h ) ) ) - log ( z ( d log ( a ) + c log ( h ) ) ) + log ( 1 d z log ( a ) + c z log ( h ) ) ) ) /; n TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] Condition z z n a d z h g c z h g z n 1 -1 z d a c h -1 n -1 -1 a d z k 0 n -1 z d a c h k Pochhammer n 1 k -1 n -1 h c z a d z k n 1 -1 -1 z d a c h k Pochhammer n 1 k -1 n -1 h c z -1 1 2 -1 n -1 -1 -1 n 2 ExpIntegralEi z d a c h 2 -1 z d a c h -1 z d a c h 1 d z a c z h -1 n [/itex]

 Rule Form

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

 2002-12-18