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.

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