Taylor Series
The digamma has a rational zeta series, given by the Taylor series at z=1. This is
- ,
which converges for |z|<1. Here, is the Riemann zeta function. This series is easily derived from the corresponding Taylor's series for the Hurwitz zeta function.
Read more about this topic: Digamma Function
Famous quotes containing the words taylor and/or series:
“the eave-drops fall
Heard only in the trances of the blast,
Or if the secret ministry of frost
Shall hang them up in silent icicles,
Quietly shining to the quiet Moon.”
—Samuel Taylor Coleridge (1772–1834)
“Life ... is not simply a series of exciting new ventures. The future is not always a whole new ball game. There tends to be unfinished business. One trails all sorts of things around with one, things that simply won’t be got rid of.”
—Anita Brookner (b. 1928)