In mathematics, formal power series are a generalization of polynomials as formal objects, where the number of terms is allowed to be infinite; this implies giving up the possibility to substitute arbitrary values for indeterminates. This perspective contrasts with that of power series, whose variables designate numerical values, and which series therefore only have a definite value if convergence can be established. Formal power series are often used merely to represent the whole collection of their coefficients. In combinatorics, they provide representations of numerical sequences and of multisets, and for instance allow giving concise expressions for recursively defined sequences regardless of whether the recursion can be explicitly solved; this is known as the method of generating functions.
Read more about Formal Power Series: Introduction, The Ring of Formal Power Series, Applications, Interpreting Formal Power Series As Functions, Examples and Related Topics
Famous quotes containing the words formal, power and/or series:
“The bed is now as public as the dinner table and governed by the same rules of formal confrontation.”
—Angela Carter (1940–1992)
“Fear death?—to feel the fog in my throat,
The mist in my face,
When the snows begin, and the blasts denote
I am nearing the place,
The power of the night, the press of the storm,
The post of the foe;
Where he stands, the Arch Fear in a visible form,
Yet the strong man must go:”
—Robert Browning (1812–1889)
“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)