List of Maclaurin Series of Some Common Functions
- See also List of mathematical series
Several important Maclaurin series expansions follow. All these expansions are valid for complex arguments x.
Exponential function:
Natural logarithm:
Finite geometric series:
Infinite geometric series:
Variants of the infinite geometric series:
Square root:
Binomial series (includes the square root for α = 1/2 and the infinite geometric series for α = −1):
with generalized binomial coefficients
Trigonometric functions:
Hyperbolic functions:
The numbers Bk appearing in the summation expansions of tan(x) and tanh(x) are the Bernoulli numbers. The Ek in the expansion of sec(x) are Euler numbers.
Read more about this topic: Taylor Series
Famous quotes containing the words list of, list, series, common and/or functions:
“Do your children view themselves as successes or failures? Are they being encouraged to be inquisitive or passive? Are they afraid to challenge authority and to question assumptions? Do they feel comfortable adapting to change? Are they easily discouraged if they cannot arrive at a solution to a problem? The answers to those questions will give you a better appraisal of their education than any list of courses, grades, or test scores.”
—Lawrence Kutner (20th century)
“Feminism is an entire world view or gestalt, not just a laundry list of womens issues.”
—Charlotte Bunch (b. 1944)
“Rosalynn said, Jimmy, if we could only get Prime Minister Begin and President Sadat up here on this mountain for a few days, I believe they might consider how they could prevent another war between their countries. That gave me the idea, and a few weeks later, I invited both men to join me for a series of private talks. In September 1978, they both came to Camp David.”
—Jimmy Carter (James Earl Carter, Jr.)
“The course of my long life hath reached at last
In fragile bark oer a tempestuous sea
The common harbor, where must rendered be
Account for all the actions of the past.”
—Henry Wadsworth Longfellow (18071882)
“If photography is allowed to stand in for art in some of its functions it will soon supplant or corrupt it completely thanks to the natural support it will find in the stupidity of the multitude. It must return to its real task, which is to be the servant of the sciences and the arts, but the very humble servant, like printing and shorthand which have neither created nor supplanted literature.”
—Charles Baudelaire (18211867)