The logarithmic integral is defined by

(1) |

(2) | |||

(3) | |||

(4) |

where is the Exponential Integral. (Note that the Notation is also used for the Polylogarithm.) Nielsen (1965, pp. 3 and 11) showed and Ramanujan independently discovered (Berndt 1994) that

(5) |

(6) |

**References**

Berndt, B. C. *Ramanujan's Notebooks, Part IV.* New York: Springer-Verlag, pp. 126-131, 1994.

Nielsen, N. *Theorie des Integrallogarithms.* New York: Chelsea, 1965.

Vardi, I. *Computational Recreations in Mathematica.* Reading, MA: Addison-Wesley, p. 151, 1991.

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1999-05-25