### 15.5 Exponential Integrals

The Exponential Integral and related functions 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

  Categories:Exponential Integrals ·Special functions ·

Function: expintegral_ei (z)

  The Exponential Integral Ei(z) (A&S 5.1.2)

  Categories:Exponential Integrals ·Special functions ·

Function: expintegral_li (z)

  The Exponential Integral Li(z) (A&S 5.1.3)

  Categories:Exponential Integrals ·Special functions ·

Function: expintegral_e (n,z)

  The Exponential Integral En(z) (A&S 5.1.4) defined as

  Categories:Exponential Integrals ·Special functions ·

Function: expintegral_si (z)

  The Exponential Integral Si(z) (A&S 5.2.1) defined as

  Categories:Exponential Integrals ·Special functions ·

Function: expintegral_ci (z)

  The Exponential Integral Ci(z) (A&S 5.2.2) defined as

  Categories:Exponential Integrals ·Special functions ·

Function: expintegral_shi (z)

  The Exponential Integral Shi(z) (A&S 5.2.3) defined as

  Categories:Exponential Integrals ·Special functions ·

Function: expintegral_chi (z)

  The Exponential Integral Chi(z) (A&S 5.2.4) defined as

  Categories:Exponential Integrals ·Special functions ·

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.

  Categories:Exponential Integrals ·

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

  Categories:Exponential Integrals ·