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Re: int(exp(x^n),x) and Ei

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In article <0q6dnULAAoXiA43SnZ2dnUVZ_oWdnZ2d@megapath.net>, Thomas D.
Dean <tomdean@speakeasy.org> wrote:

> Wolfram gives the result of
> 
> integrate(exp(x^n),x) as
> 
> integrate(exp(x^n),x) = -x*Ei[(n-1)/n](-x^n)/n
> 
> http://integrals.wolfram.com/index.jsp?expr=exp(x^n)&random=false
> 
> Maple just returns the original expression.
> 
> How do I get the Ei form?

I think you cannot do that in Maple.  That E with subscript is just a
re-writing of the original integral anyway... and Maple does not
include that variant.  Using an actual value for n, Maple can produce
the incomplete Gamma versions...

integrate(exp(x^7),x)
after simplifying gets me to
(1/7)*exp(-((1/7)*I)*Pi)*(GAMMA(1/7)-GAMMA(1/7, -x^7))
and you can of course adjust the constant of integration.
So, interestingly, both Maple and Alpha use complex numbers to
represent this real integral.

-- 
G. A. Edgar                              http://www.math.ohio-state.edu/~edgar/

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Thread

int(exp(x^n),x) and Ei "Thomas D. Dean" <tomdean@speakeasy.org> - 2012-01-13 13:13 -0800
  Re: int(exp(x^n),x) and Ei Axel Vogt <&noreply@axelvogt.de> - 2012-01-14 09:17 +0100
  Re: int(exp(x^n),x) and Ei "G. A. Edgar" <edgar@math.ohio-state.edu.invalid> - 2012-01-14 06:59 -0700
  Re: int(exp(x^n),x) and Ei Peter Pein <petsie@dordos.net> - 2012-01-14 20:40 +0100
    Re: int(exp(x^n),x) and Ei "G. A. Edgar" <edgar@math.ohio-state.edu.invalid> - 2012-01-15 06:45 -0700

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