Logarithmic Integral Function - Special Values

Special Values

The function li(x) has a single positive zero; it occurs at x ≈ 1.45136 92348 ...; this number is known as the Ramanujan–Soldner constant.

li(2) ≈ 1.045163 780117 492784 844588 889194 613136 522615 578151…

This is where is the incomplete gamma function. It must be understood as the Cauchy principal value of the function.

Read more about this topic:  Logarithmic Integral Function

Famous quotes containing the words special and/or values:

    O my Brothers! love your Country. Our Country is our home, the home which God has given us, placing therein a numerous family which we love and are loved by, and with which we have a more intimate and quicker communion of feeling and thought than with others; a family which by its concentration upon a given spot, and by the homogeneous nature of its elements, is destined for a special kind of activity.
    Giuseppe Mazzini (1805–1872)

    With all of its bad influences, T.V. is not to be feared.... It can be a fairly safe laboratory for confronting, seeing through, and thus being immunized against unhealthy values so as to be “in the world but not of it.”
    Polly Berrien Berends (20th century)