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  2. Generating function - Wikipedia

    en.wikipedia.org/wiki/Generating_function

    In mathematics, a generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series.Generating functions are often expressed in closed form (rather than as a series), by some expression involving operations on the formal series.

  3. Dirichlet series inversion - Wikipedia

    en.wikipedia.org/wiki/Dirichlet_series_inversion

    In analytic number theory, a Dirichlet series, or Dirichlet generating function (DGF), of a sequence is a common way of understanding and summing arithmetic functions in a meaningful way. A little known, or at least often forgotten about, way of expressing formulas for arithmetic functions and their summatory functions is to perform an integral ...

  4. Lagrange inversion theorem - Wikipedia

    en.wikipedia.org/wiki/Lagrange_inversion_theorem

    Faà di Bruno's formula gives coefficients of the composition of two formal power series in terms of the coefficients of those two series. Equivalently, it is a formula for the nth derivative of a composite function. Lagrange reversion theorem for another theorem sometimes called the inversion theorem; Formal power series#The Lagrange inversion ...

  5. Category of preordered sets - Wikipedia

    en.wikipedia.org/wiki/Category_of_preordered_sets

    There are thus no zero objects in Ord. The categorical product in Ord is given by the product order on the cartesian product. We have a forgetful functor Ord → Set that assigns to each preordered set the underlying set, and to each order-preserving function the underlying function. This functor is faithful, and therefore Ord is a concrete ...

  6. List of mathematical series - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_series

    An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.

  7. Computational complexity of mathematical operations - Wikipedia

    en.wikipedia.org/wiki/Computational_complexity...

    The complexity of an elementary function is equivalent to that of its inverse, since all elementary functions are analytic and hence invertible by means of Newton's method. In particular, if either exp {\displaystyle \exp } or log {\displaystyle \log } in the complex domain can be computed with some complexity, then that complexity is ...

  8. Yes, nearly everyone snores, but you can stop it. Here's how.

    www.aol.com/yes-nearly-everyone-snores-stop...

    Few involuntary behaviors feel as off-putting as snoring.The telltale low, vibrating rattle emitting from an open mouth is not exactly the sound or image we want on display when a friend or new ...

  9. Order type - Wikipedia

    en.wikipedia.org/wiki/Order_type

    In mathematics, especially in set theory, two ordered sets X and Y are said to have the same order type if they are order isomorphic, that is, if there exists a bijection (each element pairs with exactly one in the other set) : such that both f and its inverse are monotonic (preserving orders of elements).