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:
“A mans interest in a single bluebird is worth more than a complete but dry list of the fauna and flora of a town.”
—Henry David Thoreau (18171862)
“Religious literature has eminent examples, and if we run over our private list of poets, critics, philanthropists and philosophers, we shall find them infected with this dropsy and elephantiasis, which we ought to have tapped.”
—Ralph Waldo Emerson (18031882)
“Every day the fat woman dies a series of small deaths.”
—Shelley Bovey, U.S. author. Being Fat Is Not a Sin, ch. 1 (1989)
“The inspired scribbler always has the gift for gossip in our common usage ... he or she can always inspire the commonplace with an uncommon flavor, and transform trivialities by some original grace or sympathy or humor or affection.”
—Elizabeth Drew (18871965)
“The English masses are lovable: they are kind, decent, tolerant, practical and not stupid. The tragedy is that there are too many of them, and that they are aimless, having outgrown the servile functions for which they were encouraged to multiply. One day these huge crowds will have to seize power because there will be nothing else for them to do, and yet they neither demand power nor are ready to make use of it; they will learn only to be bored in a new way.”
—Cyril Connolly (19031974)