Harmonic Number - Special Values For Fractional Arguments

Special Values For Fractional Arguments

There are the following special analytic values for fractional arguments between 0 and 1, given by the integral

More may be generated from the recurrence relation or from the reflection relation .

For every, integer or not, we have:

Based on, we have:, where is the Euler–Mascheroni constant or, more generally, for every n we have:

Read more about this topic:  Harmonic Number

Famous quotes containing the words special, values, fractional and/or arguments:

    The great rule: If the little bit you have is nothing special in itself, at least find a way of saying it that is a little bit special.
    —G.C. (Georg Christoph)

    Postmodernity is the simultaneity of the destruction of earlier values and their reconstruction. It is renovation within ruination.
    Jean Baudrillard (b. 1929)

    Hummingbird
    stay for a fractional sharp
    sweetness, and’s gone, can’t take
    more than that.
    Denise Levertov (b. 1923)

    We are seeing an increasing level of attacks on the “selfishness” of women. There are allegations that all kinds of social ills, from runaway children to the neglected elderly, are due to the fact that women have left their “rightful” place in the home. Such arguments are simplistic and wrongheaded but women are especially vulnerable to the accusation that if society has problems, it’s because women aren’t nurturing enough.
    Grace Baruch (20th century)