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In set theory, the notation is used to denote the set of functions from the set to the set . Currying is the natural bijection between the set A B × C {\displaystyle A^{B\times C}} of functions from B × C {\displaystyle B\times C} to A {\displaystyle A} , and the set ( A C ) B {\displaystyle (A^{C})^{B}} of functions from B {\displaystyle B ...
The sieve led to a series of important breakthroughs in analytic number theory. It is named after the mathematicians Dan Goldston, János Pintz and Cem Yıldırım. [1] They used it in 2005 to show that there are infinitely many prime tuples whose distances are arbitrarily smaller than the average distance that follows from the prime number ...
Pandas (styled as pandas) is a software library written for the Python programming language for data manipulation and analysis. In particular, it offers data structures and operations for manipulating numerical tables and time series. It is free software released under the three-clause BSD license. [2]
Wes McKinney is an American software developer and businessman. He is the creator and "Benevolent Dictator for Life" (BDFL) of the open-source pandas package for data analysis in the Python programming language, and has also authored three versions of the reference book Python for Data Analysis.
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.
In statistics, a power transform is a family of functions applied to create a monotonic transformation of data using power functions.It is a data transformation technique used to stabilize variance, make the data more normal distribution-like, improve the validity of measures of association (such as the Pearson correlation between variables), and for other data stabilization procedures.
Dirichlet lambda function, λ(s) = (1 – 2 −s)ζ(s) where ζ is the Riemann zeta function; Liouville function, λ(n) = (–1) Ω(n) Von Mangoldt function, Λ(n) = log p if n is a positive power of the prime p; Modular lambda function, λ(τ), a highly symmetric holomorphic function on the complex upper half-plane
The processing of transforming the lambda expression is a series of lifts. Each lift has, A sub expression chosen for it by the function lift-choice. The sub expression should be chosen so that it may be converted into an equation with no lambdas. The lift is performed by a call to the lambda-lift meta function, described in the next section,