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 Exp

 http://functions.wolfram.com/01.03.21.0576.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18