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:
“Personal prudence, even when dictated by quite other than selfish considerations, surely is no special virtue in a military man; while an excessive love of glory, impassioning a less burning impulse, the honest sense of duty, is the first.”
—Herman Melville (1819–1891)
“When the shingles hissed
in the rain incendiary,
other values were revealed to us,”
—Hilda Doolittle (1886–1961)
“Hummingbird
stay for a fractional sharp
sweetness, and’s gone, can’t take
more than that.”
—Denise Levertov (b. 1923)
“‘Tis happy, therefore, that nature breaks the force of all sceptical arguments in time, and keeps them from having any considerable influence on the understanding. Were we to trust entirely to their self-destruction, that can never take place, ‘till they have first subverted all conviction, and have totally destroy’d human reason.”
—David Hume (1711–1776)