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:

    Mr. Christian, it is about time for many people to begin to come to the White House to discuss different phases of the coal strike. When anybody comes, if his special problem concerns the state, refer him to the governor of Pennsylvania. If his problem has a national phase, refer him to the United States Coal Commission. In no event bring him to me.
    Calvin Coolidge (1872–1933)

    ... the loss of belief in future states is politically, though certainly not spiritually, the most significant distinction between our present period and the centuries before. And this loss is definite. For no matter how religious our world may turn again, or how much authentic faith still exists in it, or how deeply our moral values may be rooted in our religious systems, the fear of hell is no longer among the motives which would prevent or stimulate the actions of a majority.
    Hannah Arendt (1906–1975)

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

    Yesterday the Electoral Commission decided not to go behind the papers filed with the Vice-President in the case of Florida.... I read the arguments in the Congressional Record and can’t see how lawyers can differ on the question. But the decision is by a strictly party vote—eight Republicans against seven Democrats! It shows the strength of party ties.
    Rutherford Birchard Hayes (1822–1893)