Both are defined via Taylor series analogous to the real case.

It converges more quickly than the Taylor series, especially if z is close to 1.

Using the Sigma notation, this is also written as formula_48This series can be derived from the above Taylor series.

The above Taylor series for remains valid for complex numbers x with .

The Taylor series of ln z provides a particularly useful approximation to ln(1 z ) when z is small, _z_ 1 , since then formula_46For example, with z 0.1 the first order approximation gives ln(1.1) 0.1, which is less than 5 off the correct value 0.0953. More efficient seriesAnother series is based on the area hyperbolic tangent function formula_47for any real number z 0.

Taylor, Barbara.

' explained Taylor.

Taylor, Gary.

Taylor, A. J. P. and S. L. Mayer, eds.

Taylor, Jeff.

Am I speaking with Taylor?

Taylor Francis, 2006.

London Taylor Walton.

London Taylor Walton.

Chapman, Cleese, and Tim Brooke Taylor later joined Feldman in the television comedy series At Last the 1948 Show .

It features more than 24 regular characters from The Simpsons and features the voices of the regular cast members, as well as Pamela Hayden, Russi Taylor and Kelsey Grammer.

Am I speaking with Taylor?

Taylor, George Rogers, ed.

Taylor, Michael J.H., ed.

London Taylor, Walton Malbery.

In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.

This album features vocals by James Taylor.

1498) December John Taylor, Bishop of Lincoln (b.

In the case that , the series is also called a Maclaurin series.

Stephen King called the series a feat of which only a superior imagination is capable , and declared Rowling's punning, one eyebrow cocked sense of humor to be remarkable .

Elizabeth Taylor was incredibly beautiful.

The Origin of Species An Outline, A short, accessible outline of the book.

Thompson, Ann and Taylor, Neil.

Rush darter, E. phytophilum Bart Taylor, 1999.

Jeremy Taylor echoes her sentiment...sort of

On May 30, 2006, Taylor Hicks was named American Idol , with Katharine McPhee the runner up.

1933) 1985 Taylor Caldwell, English American author (b.

1672) December 29 Brook Taylor, English mathematician (b.

In the 14th century, Indian mathematician Madhava of Sangamagrama and the Kerala school of astronomy and mathematics stated components of calculus such as the Taylor series and infinite series approximations.

He came to prominence playing Opie Taylor in the sitcom The Andy Griffith Show for eight years, and later the teenaged Richie Cunningham in the sitcom Happy Days for six years.

Taylor does not want to go through all of that.

Taylor was raised by his single mother.

In addition to producing the EP, Taylor provided guest vocals on three of the five tracks ( Ember Drive, My Last Stand, and Addicted which Taylor co wrote).

by L. Kilian and M. P. Taylor , November 2001 .

The Mexican American War broke out in May 1846, and Taylor led American troops to victory in a series of battles culminating in the Battle of Palo Alto and the Battle of Monterrey.

Voyager producer Jeri Taylor wrote two novels featuring back story for Voyager characters, and screen authors David Gerrold, D. C. Fontana, and Melinda Snodgrass have penned books, as well.

), Doctor of Philosophy (Ph.D.), and Doctor of Education (Ed.D.).

(Athens, Georgia) in Thompson and Taylor (2006a, 127).

When , the series is also called a Maclaurin series.

Aaron Taylor Johnson signed on to play Quicksilver in the 2015 film '.