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:

    A special kind of beauty exists which is born in language, of language, and for language.
    Gaston Bachelard (1884–1962)

    Culture is the name for what people are interested in, their thoughts, their models, the books they read and the speeches they hear, their table-talk, gossip, controversies, historical sense and scientific training, the values they appreciate, the quality of life they admire. All communities have a culture. It is the climate of their civilization.
    Walter Lippmann (1889–1974)

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

    What can you do against the lunatic who is more intelligent than yourself, who gives your arguments a fair hearing and then simply persists in his lunacy.
    George Orwell (1903–1950)