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Exp






Mathematica Notation

Traditional Notation









Elementary Functions > Exp[z] > Integration > Indefinite integration > Involving functions of the direct function and a power function > Involving products of the direct function and a power function > Involving products of two direct functions and a power function > Involving znad z+e hc zr+g





http://functions.wolfram.com/01.03.21.0580.01









  


  










Input Form





Integrate[z^n a^(d z + e) h^(c Sqrt[z] + g), z] == (2^(-1 - 2 n) a^e 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







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2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> d </ci> <apply> <ci> Gamma </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <ci> j </ci> <ci> k </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> d </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ln /> <ci> a </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <apply> <ln /> <ci> h </ci> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> d </ci> <apply> <ln /> <ci> a </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> d </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ln /> <ci> a </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <apply> <ln /> <ci> h </ci> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <ci> d </ci> <apply> <ln /> <ci> a </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ln /> <ci> a </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <apply> <ci> Gamma </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <ci> j </ci> <ci> k </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> 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</semantics> </math>










Rule Form





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





2002-12-18





© 1998- Wolfram Research, Inc.