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:
“It is surely a matter of common observation that a man who knows no one thing intimately has no views worth hearing on things in general. The farmer philosophizes in terms of crops, soils, markets, and implements, the mechanic generalizes his experiences of wood and iron, the seaman reaches similar conclusions by his own special road; and if the scholar keeps pace with these it must be by an equally virile productivity.”
—Charles Horton Cooley (1864–1929)
“The return to solid values is always hard.... Distress, panic, and hard times have marked our pathway in returning to solid values.”
—James A. Garfield (1831–1881)
“Hummingbird
stay for a fractional sharp
sweetness, and’s gone, can’t take
more than that.”
—Denise Levertov (b. 1923)
“Through Plato Aristotle came to believe in God, but Plato never attempted to prove His reality. Aristotle had to do so. Plato contemplated Him; Aristotle produced arguments to demonstrate Him. Plato never defined Him, but Aristotle thought God through logically and concluded with entire satisfaction to himself that He was the Unmoved Mover.”
—Edith Hamilton (1867–1963)