Table of Contents
56 relations: Academic Press, Analytic continuation, Antiderivative, Asymptote, Asymptotic expansion, Bounded function, Branch point, Complex analysis, Complex logarithm, Computer algebra system, Confluent hypergeometric function, Constant of integration, Continuous function, Cumulative distribution function, Entire function, Error function, Euler's constant, Exponential integral, Falling and rising factorials, Fourier transform, Gamma distribution, Gamma function, Gauss's continued fraction, Hartogs's theorem on separate holomorphicity, Holomorphic function, Integer, Integral, Integration by parts, Keith Geddes, Laplace transform, Limit of a function, Line integral, Mathematics, Meijer G-function, Mellin transform, Meromorphic function, Microsoft Excel, Multiplication theorem, Multivalued function, Neighbourhood (mathematics), Permutation, Poisson distribution, Power series, Principal branch, Python (programming language), Reciprocal gamma function, Recurrence relation, Riemann surface, Scale parameter, SciPy, ... Expand index (6 more) »
- Continued fractions
- Gamma and related functions
Academic Press
Academic Press (AP) is an academic book publisher founded in 1941.
See Incomplete gamma function and Academic Press
Analytic continuation
In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of definition of a given analytic function.
See Incomplete gamma function and Analytic continuation
Antiderivative
In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral of a function is a differentiable function whose derivative is equal to the original function.
See Incomplete gamma function and Antiderivative
Asymptote
In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity.
See Incomplete gamma function and Asymptote
Asymptotic expansion
In mathematics, an asymptotic expansion, asymptotic series or Poincaré expansion (after Henri Poincaré) is a formal series of functions which has the property that truncating the series after a finite number of terms provides an approximation to a given function as the argument of the function tends towards a particular, often infinite, point.
See Incomplete gamma function and Asymptotic expansion
Bounded function
In mathematics, a function f defined on some set X with real or complex values is called bounded if the set of its values is bounded.
See Incomplete gamma function and Bounded function
Branch point
In the mathematical field of complex analysis, a branch point of a multivalued function is a point such that if the function is n-valued (has n values) at that point, all of its neighborhoods contain a point that has more than n values.
See Incomplete gamma function and Branch point
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.
See Incomplete gamma function and Complex analysis
Complex logarithm
In mathematics, a complex logarithm is a generalization of the natural logarithm to nonzero complex numbers.
See Incomplete gamma function and Complex logarithm
Computer algebra system
A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists.
See Incomplete gamma function and Computer algebra system
Confluent hypergeometric function
In mathematics, a confluent hypergeometric function is a solution of a confluent hypergeometric equation, which is a degenerate form of a hypergeometric differential equation where two of the three regular singularities merge into an irregular singularity.
See Incomplete gamma function and Confluent hypergeometric function
Constant of integration
In calculus, the constant of integration, often denoted by C (or c), is a constant term added to an antiderivative of a function f(x) to indicate that the indefinite integral of f(x) (i.e., the set of all antiderivatives of f(x)), on a connected domain, is only defined up to an additive constant.
See Incomplete gamma function and Constant of integration
Continuous function
In mathematics, a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function.
See Incomplete gamma function and Continuous function
Cumulative distribution function
In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. Every probability distribution supported on the real numbers, discrete or "mixed" as well as continuous, is uniquely identified by a right-continuous monotone increasing function (a càdlàg function) F \colon \mathbb R \rightarrow satisfying \lim_F(x).
See Incomplete gamma function and Cumulative distribution function
Entire function
In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic on the whole complex plane.
See Incomplete gamma function and Entire function
Error function
In mathematics, the error function (also called the Gauss error function), often denoted by, is a function defined as: \operatorname z.
See Incomplete gamma function and Error function
Euler's constant
Euler's constant (sometimes called the Euler–Mascheroni constant) is a mathematical constant, usually denoted by the lowercase Greek letter gamma, defined as the limiting difference between the harmonic series and the natural logarithm, denoted here by: \begin \gamma &.
See Incomplete gamma function and Euler's constant
Exponential integral
In mathematics, the exponential integral Ei is a special function on the complex plane.
See Incomplete gamma function and Exponential integral
Falling and rising factorials
In mathematics, the falling factorial (sometimes called the descending factorial, falling sequential product, or lower factorial) is defined as the polynomial \begin (x)_n. Incomplete gamma function and falling and rising factorials are gamma and related functions.
See Incomplete gamma function and Falling and rising factorials
Fourier transform
In physics, engineering and mathematics, the Fourier transform (FT) is an integral transform that takes a function as input and outputs another function that describes the extent to which various frequencies are present in the original function.
See Incomplete gamma function and Fourier transform
Gamma distribution
In probability theory and statistics, the gamma distribution is a versatile two-parameter family of continuous probability distributions. Incomplete gamma function and gamma distribution are gamma and related functions.
See Incomplete gamma function and Gamma distribution
Gamma function
In mathematics, the gamma function (represented by, the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. Incomplete gamma function and gamma function are gamma and related functions.
See Incomplete gamma function and Gamma function
Gauss's continued fraction
In complex analysis, Gauss's continued fraction is a particular class of continued fractions derived from hypergeometric functions. Incomplete gamma function and Gauss's continued fraction are continued fractions.
See Incomplete gamma function and Gauss's continued fraction
Hartogs's theorem on separate holomorphicity
In mathematics, Hartogs's theorem is a fundamental result of Friedrich Hartogs in the theory of several complex variables.
See Incomplete gamma function and Hartogs's theorem on separate holomorphicity
Holomorphic function
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood of each point in a domain in complex coordinate space.
See Incomplete gamma function and Holomorphic function
Integer
An integer is the number zero (0), a positive natural number (1, 2, 3,...), or the negation of a positive natural number (−1, −2, −3,...). The negations or additive inverses of the positive natural numbers are referred to as negative integers.
See Incomplete gamma function and Integer
Integral
In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations.
See Incomplete gamma function and Integral
Integration by parts
In calculus, and more generally in mathematical analysis, integration by parts or partial integration is a process that finds the integral of a product of functions in terms of the integral of the product of their derivative and antiderivative.
See Incomplete gamma function and Integration by parts
Keith Geddes
Keith Oliver Geddes (born 1947) is a professor emeritus in the David R. Cheriton School of Computer Science within the Faculty of Mathematics at the University of Waterloo in Waterloo, Ontario.
See Incomplete gamma function and Keith Geddes
Laplace transform
In mathematics, the Laplace transform, named after Pierre-Simon Laplace, is an integral transform that converts a function of a real variable (usually t, in the time domain) to a function of a complex variable s (in the complex-valued frequency domain, also known as s-domain, or s-plane).
See Incomplete gamma function and Laplace transform
Limit of a function
Although the function is not defined at zero, as becomes closer and closer to zero, becomes arbitrarily close to 1.
See Incomplete gamma function and Limit of a function
Line integral
In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve.
See Incomplete gamma function and Line integral
Mathematics
Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.
See Incomplete gamma function and Mathematics
Meijer G-function
In mathematics, the G-function was introduced by as a very general function intended to include most of the known special functions as particular cases.
See Incomplete gamma function and Meijer G-function
Mellin transform
In mathematics, the Mellin transform is an integral transform that may be regarded as the multiplicative version of the two-sided Laplace transform.
See Incomplete gamma function and Mellin transform
Meromorphic function
In the mathematical field of complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all of D except for a set of isolated points, which are poles of the function.
See Incomplete gamma function and Meromorphic function
Microsoft Excel
Microsoft Excel is a spreadsheet editor developed by Microsoft for Windows, macOS, Android, iOS and iPadOS.
See Incomplete gamma function and Microsoft Excel
Multiplication theorem
In mathematics, the multiplication theorem is a certain type of identity obeyed by many special functions related to the gamma function. Incomplete gamma function and multiplication theorem are gamma and related functions.
See Incomplete gamma function and Multiplication theorem
Multivalued function
In mathematics, a multivalued function (also known as a multiple-valued function) is a function that has two or more values in its range for at least one point in its domain.
See Incomplete gamma function and Multivalued function
Neighbourhood (mathematics)
In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space.
See Incomplete gamma function and Neighbourhood (mathematics)
Permutation
In mathematics, a permutation of a set can mean one of two different things.
See Incomplete gamma function and Permutation
Poisson distribution
In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time if these events occur with a known constant mean rate and independently of the time since the last event.
See Incomplete gamma function and Poisson distribution
Power series
In mathematics, a power series (in one variable) is an infinite series of the form \sum_^\infty a_n \left(x - c\right)^n.
See Incomplete gamma function and Power series
Principal branch
In mathematics, a principal branch is a function which selects one branch ("slice") of a multi-valued function.
See Incomplete gamma function and Principal branch
Python (programming language)
Python is a high-level, general-purpose programming language.
See Incomplete gamma function and Python (programming language)
Reciprocal gamma function
In mathematics, the reciprocal gamma function is the function where denotes the gamma function. Incomplete gamma function and reciprocal gamma function are gamma and related functions.
See Incomplete gamma function and Reciprocal gamma function
Recurrence relation
In mathematics, a recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms.
See Incomplete gamma function and Recurrence relation
Riemann surface
In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold.
See Incomplete gamma function and Riemann surface
Scale parameter
In probability theory and statistics, a scale parameter is a special kind of numerical parameter of a parametric family of probability distributions.
See Incomplete gamma function and Scale parameter
SciPy
SciPy (pronounced "sigh pie") is a free and open-source Python library used for scientific computing and technical computing.
See Incomplete gamma function and SciPy
Shape parameter
In probability theory and statistics, a shape parameter (also known as form parameter) is a kind of numerical parameter of a parametric family of probability distributions that is neither a location parameter nor a scale parameter (nor a function of these, such as a rate parameter).
See Incomplete gamma function and Shape parameter
Singularity (mathematics)
In mathematics, a singularity is a point at which a given mathematical object is not defined, or a point where the mathematical object ceases to be well-behaved in some particular way, such as by lacking differentiability or analyticity.
See Incomplete gamma function and Singularity (mathematics)
Special functions
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.
See Incomplete gamma function and Special functions
Spreadsheet
A spreadsheet is a computer application for computation, organization, analysis and storage of data in tabular form.
See Incomplete gamma function and Spreadsheet
Symbolic integration
In calculus, symbolic integration is the problem of finding a formula for the antiderivative, or indefinite integral, of a given function f(x), i.e. to find a formula for a differentiable function F(x) such that This is also denoted.
See Incomplete gamma function and Symbolic integration
Uniform convergence
In the mathematical field of analysis, uniform convergence is a mode of convergence of functions stronger than pointwise convergence.
See Incomplete gamma function and Uniform convergence
See also
Continued fractions
- Chain sequence
- Complete quotient
- Continuant (mathematics)
- Continued fraction
- Convergence problem
- Engel expansion
- Euler's continued fraction formula
- Gauss's continued fraction
- Gauss–Kuzmin distribution
- Gauss–Kuzmin–Wirsing operator
- Gaussian brackets
- Generalized continued fraction
- Hermite's problem
- Incomplete gamma function
- Khinchin's constant
- Lévy's constant
- List of mathematical constants
- Lochs's theorem
- Markov constant
- Metallic means
- Minkowski's question-mark function
- Padé approximant
- Padé table
- Pell's equation
- Periodic continued fraction
- Restricted partial quotients
- Rogers–Ramanujan continued fraction
- Solving quadratic equations with continued fractions
- Stern–Brocot tree
- Stieltjes transformation
- Śleszyński–Pringsheim theorem
Gamma and related functions
- Balanced polygamma function
- Barnes G-function
- Beta function
- Bohr–Mollerup theorem
- Chebyshev integral
- Chowla–Selberg formula
- Digamma function
- Elliptic gamma function
- Euler integral
- Factorial
- Falling and rising factorials
- Fransén–Robinson constant
- Gamma distribution
- Gamma function
- Gautschi's inequality
- Generalized Pochhammer symbol
- Generalized gamma distribution
- Hölder's theorem
- Hadamard's gamma function
- Incomplete gamma function
- Inverse gamma function
- Inverse-gamma distribution
- K-function
- Lanczos approximation
- Multiple gamma function
- Multiplication theorem
- Multivariate gamma function
- Nu function
- Particular values of the gamma function
- Pochhammer k-symbol
- Polygamma function
- Q-gamma function
- Reciprocal gamma function
- Spouge's approximation
- Stirling's approximation
- Trigamma function
- Wielandt theorem
References
Also known as Derivatives of the incomplete gamma function, Gamma incomplete, Incomplete Gamma-function, Lower incomplete gamma function, Regularized Gamma function, Upper incomplete gamma function.