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Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications [1] the lerch transcendent, is given by: The term is defined by consensus, and thus lacks a general formal definition, but the list of mathematical functions contains functions that are commonly accepted as special.
[3] the predecessor of numpy, numeric, was originally created by jim hugunin with contributions from several other developers It is named after czech mathematician mathias lerch, who published a paper about a similar function in 1887 List of mathematical functions in mathematics, some functions or groups of functions are important enough to deserve their own names
This is a listing of articles which explain some of these functions in more detail
There is a large theory of special functions which developed out of statistics and mathematical physics. This is a list of special function eponyms in mathematics, to cover the theory of special functions, the differential equations they satisfy, named differential operators of the theory (but not intended to include every mathematical eponym) Named symmetric functions, and other special polynomials, are included. Pages in category special functions the following 144 pages are in this category, out of 144 total
This list may not reflect recent changes. Category:elementary special functions special functions that are elementary, that is, built from a finite number of exponentials, logarithms, constants, one variable, and roots of equations through composition and combinations using the four elementary operations (+ − × ÷). In mathematics, the upper and lower incomplete gamma functions are types of special functions which arise as solutions to various mathematical problems such as certain integrals Their respective names stem from their integral definitions, which are defined similarly to the gamma function but with different or incomplete integral limits.
In mathematics, the polylogarithm (also known as jonquière's function, for alfred jonquière) is a special function lis(z) of order s and argument z
Only for special values of s does the polylogarithm reduce to an elementary function such as the natural logarithm or a rational function In quantum statistics, the polylogarithm function appears as the closed form of integrals of the fermi. Generalized hypergeometric functions include the (gaussian) hypergeometric function and the confluent hypergeometric function as special cases, which in turn have many particular special functions as special cases, such as elementary functions, bessel functions, and the classical orthogonal polynomials. Lerch transcendent in mathematics, the lerch transcendent, is a special function that generalizes the hurwitz zeta function and the polylogarithm
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