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:
“There is special providence in the fall of a sparrow. If it be now, ‘tis not to come; if it be not to come, it will be
now; if it be not now, yet it will come—the readiness is
all.”
—William Shakespeare (1564–1616)
“What we often take to be family values—the work ethic, honesty, clean living, marital fidelity, and individual responsibility—are in fact social, religious, or cultural values. To be sure, these values are transmitted by parents to their children and are familial in that sense. They do not, however, originate within the family. It is the value of close relationships with other family members, and the importance of these bonds relative to other needs.”
—David Elkind (20th century)
“Hummingbird
stay for a fractional sharp
sweetness, and’s gone, can’t take
more than that.”
—Denise Levertov (b. 1923)
“Argument is conclusive ... but ... it does not remove doubt, so that the mind may rest in the sure knowledge of the truth, unless it finds it by the method of experiment.... For if any man who never saw fire proved by satisfactory arguments that fire burns ... his hearer’s mind would never be satisfied, nor would he avoid the fire until he put his hand in it ... that he might learn by experiment what argument taught.”
—Roger Bacon (c. 1214–1294)