(maxima.info)Exponential Integrals

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15.5 Exponential Integrals
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The Exponential Integral and related funtions are defined in Abramowitz
and Stegun, Handbook of Mathematical Functions, Chapter 5

 -- Function: expintegral_e1 (<z>)
     The Exponential Integral E1(z) (A&S 5.1.1) defined as

     integrate(exp(-t)/t, t, z, inf) with abs(arg z) < %pi.

 -- Function: expintegral_ei (<z>)
     The Exponential Integral Ei(z) (A&S 5.1.2)

 -- Function: expintegral_li (<z>)
     The Exponential Integral Li(z) (A&S 5.1.3)

 -- Function: expintegral_e (<n>,<z>)
     The Exponential Integral En(z) (A&S 5.1.4) defined as

     integrate(exp(-z*t)/t^n, t, 1, inf) with real(x) > 1 and n a
     non-negative integer.

 -- Function: expintegral_si (<z>)
     The Exponential Integral Si(z) (A&S 5.2.1) defined as

     integrate(sin(t)/t, t, 0, z)

 -- Function: expintegral_ci (<z>)
     The Exponential Integral Ci(z) (A&S 5.2.2) defined as

     %gamma + log(z) + integrate((cos(t) - 1)/t, t, 0, z)

     with abs(arg z) < %pi

 -- Function: expintegral_shi (<z>)
     The Exponential Integral Shi(z) (A&S 5.2.3) defined as

     integrate(sinh(t)/t, t, 0, z)

 -- Function: expintegral_chi (<z>)
     The Exponential Integral Chi(z) (A&S 5.2.4) defined as

     %gamma + log(z) + integrate((cosh(t) - 1)/t, t, 0, z)

     with abs(arg z) < %pi

 -- Option variable: expintrep
     Default value: false

     Change the representation of one of the exponential integrals,
     <expintegral_e(m, z)>, <expintegral_e1>, or <expintegral_ei> to an
     equivalent form if possible.

     Possible values for <expintrep> are <false>, <gamma_incomplete>,
     <expintegral_e1>, <expintegral_ei>, <expintegral_li>,
     <expintegral_trig>, or <expintegral_hyp>.

     <false> means that the representation is not changed.  Other values
     indicate the representation is to be changed to use the function
     specified where <expintegral_trig> means <expintegral_si>,
     <expintegral_ci>, and <expintegral_hyp> means <expintegral_shi> or
     <expintegral_chi>.

 -- Option variable: expintexpand
     Default value: false

     Expand the Exponential Integral E[n](z) for half integral values in
     terms of Erfc or Erf and for positive integers in terms of Ei