Newton Series
The formula is sometimes given in one of these - slightly different - forms
which represent a special cases of the more general rule
both result from iterated application of the initial formula. The auxiliary quantities are Newton series:
and
A remarkable, particular result is the noteworthy identity
Here, is the binomial coefficient.
Read more about this topic: Summation By Parts
Famous quotes containing the words newton and/or series:
“Glorious things of thee are spoken, Zion city of our God!
He, whose word cannot be broken, Formd for thee his own abode:
On the rock of ages founded, What can shake thy sure repose?
With salvations walls surrounded Thou mayst smile at all thy foes.”
—John Newton (17251807)
“Galileo, with an operaglass, discovered a more splendid series of celestial phenomena than anyone since.”
—Ralph Waldo Emerson (18031882)