Taylor Series - List of Maclaurin Series of Some Common Functions

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:

    “Modern tourist guides have helped raised tourist expectations. And they have provided the natives—from Kaiser Wilhelm down to the villagers of Chichacestenango—with a detailed and itemized list of what is expected of them and when. These are the up-to- date scripts for actors on the tourists’ stage.”
    —Daniel J. Boorstin (b. 1914)

    “Modern tourist guides have helped raised tourist expectations. And they have provided the natives—from Kaiser Wilhelm down to the villagers of Chichacestenango—with a detailed and itemized list of what is expected of them and when. These are the up-to- date scripts for actors on the tourists’ stage.”
    —Daniel J. Boorstin (b. 1914)

    “There is in every either-or a certain naivete which may well befit the evaluator, but ill- becomes the thinker, for whom opposites dissolve in series of transitions.”
    —Robert Musil (1880–1942)

    “There is all the poetry in the world in a name. It is a poem which the mass of men hear and read. What is poetry in the common sense, but a hearing of such jingling names? I want nothing better than a good word. The name of a thing may easily be more than the thing itself to me.”
    —Henry David Thoreau (1817–1862)

    “When Western people train the mind, the focus is generally on the left hemisphere of the cortex, which is the portion of the brain that is concerned with words and numbers. We enhance the logical, bounded, linear functions of the mind. In the East, exercises of this sort are for the purpose of getting in tune with the unconscious—to get rid of boundaries, not to create them.”
    —Edward T. Hall (b. 1914)