
	Where results make sense

Topic: Gamma function

Related Topics

List of mathematical functions

List of functions

Meromorphic function

Theta function

Incomplete gamma function

Elliptic function

Airy function

Beta function

Factorial function

Holomorphic function

Riemann zeta function

Bessel function

Error function

List of integrals of area functions

Exponential function

	Function (mathematics) - Wikipedia, the free encyclopedia
		A function is officially defined as a binary relation f with the property that for each element x of the domain of f there is one and only one element y of the codomain of f such that x is related by f to y.
		For this type of function, one can talk about limits and derivatives; both are measurements of the output or the change in the output as it depends on the input or the change in the input.
		The number of computable functions from integers to integers is countable, because the number of possible algorithms is. The number of all functions from integers to integers is higher: the same as the cardinality of the real numbers.
	en.wikipedia.org /wiki/Function_(mathematics) (3307 words)

	Incomplete gamma function - Wikipedia, the free encyclopedia
		In mathematics, the gamma function is defined by a definite integral.
		The incomplete gamma function is defined by an indefinite integral of the same integrand.
		There are two varieties of the incomplete gamma function, one for the case that the lower limit of integration is variable, and one for the upper limit of integration.
	en.wikipedia.org /wiki/Incomplete_gamma_function (228 words)

	Gamma correction - Wikipedia, the free encyclopedia
		A gamma characteristic is a power-law relationship that approximates the relationship between the encoded luminance in a television system and the actual desired image brightness.
		A similar, older term is used in photography to characterise the straight-line region of the Hurter-Driffield curve, which is a plot of (density or log(opacity)) of the film image versus log(exposure) for the film.
		On most displays (i.e., those with a standard gamma of 2.5), one can observe that the linear-intensity scale has a large jump in perceived brightness between the intensity values 0.0 and 0.1, while the steps at the higher end of the scale are hardly perceptible.
	en.wikipedia.org /wiki/Gamma_correction (906 words)

	Gamma function - Wikipedia, the free encyclopedia
		The derivatives of the Gamma function are described in terms of the polygamma function.
		The Bohr-Mollerup theorem states that among all functions extending the factorial functions to the positive real numbers, only the Gamma function is log-convex, that is, its natural logarithm is convex.
		The derivative of the logarithm of the Gamma function is called the digamma function; higher derivatives are the polygamma functions.
	en.wikipedia.org /wiki/Gamma_function (612 words)

	Factorial - Wikipedia, the free encyclopedia
		The Gamma function is in fact defined for all complex numbers z except for the nonpositive integers (z = 0, −1, −2, −3, ...) where it goes to infinity.
		The Gamma function is generally used in a context similar to that of the factorials (but, of course, where a more general domain is of interest).
		The Gamma function is the only function which satisfies the mentioned recursive relationship for the domain of complex numbers and is holomorphic and whose restriction to the positive real axis is log-convex.
	en.wikipedia.org /wiki/Factorial (1170 words)

	PlanetMath: gamma function
		Some values of the gamma function for small arguments are:
		The gamma function has a meromorphic continuation to the entire complex plane with poles at the non-positive integers.
		This is version 11 of gamma function, born on 2001-11-17, modified 2005-01-12.
	planetmath.org /encyclopedia/GammaFunction.html (118 words)

	Paul Godfrey on the Lanczos Implementation of the Gamma Function - Numericana
		The first document is a Matlab implementation of the complex Gamma function good to 13 digits everywhere in the complex plane.
		For a practical Gamma function, one could always fall back on the definition of the factorial function to provide exact integer results whenever z is a positive integer.
		Conclusion The convergent expansion of the Gamma function due to Lanczos is examined.
	home.att.net /~numericana/answer/info/godfrey.htm (1100 words)

	1.3.6.6.11. Gamma Distribution
		Since the general form of probability functions can be expressed in terms of the standard distribution, all subsequent formulas in this section are given for the standard form of the function.
		The formula for the percent point function of the gamma distribution does not exist in a simple closed form.
		The formula for the survival function of the gamma distribution is
	www.itl.nist.gov /div898/handbook/eda/section3/eda366b.htm (356 words)

	gamma function (Site not responding. Last check: 2007-11-06)
		x) can be seen as a generalization of the factorial: for a positive integer the function value of the gamma function is equal to the factorial.
		The function plays a major role in difference equations, as the exponential functions has its role for differential equations.
		Because of the work of Euler on the curve the function is also called the Euler gamma function or the second Euler function.
	www.2dcurves.com /gamma/gammae.html (160 words)

	PlanetMath: multivariate Gamma function (real-valued)
		The real-valued multivariate Gamma function is defined by
		The real-valued multivariate Gamma function can also be expressed in terms of the gamma function as follows
		This is version 10 of multivariate Gamma function (real-valued), born on 2004-05-13, modified 2005-11-10.
	planetmath.org /encyclopedia/GammaFunctionMultivariateReal.html (89 words)

	PlanetMath: multivariate Gamma function (complex-valued)
		The complex multivariate Gamma function is defined as
		It can also be expressed in terms of the gamma function as follows
		This is version 7 of multivariate Gamma function (complex-valued), born on 2004-05-13, modified 2004-05-14.
	planetmath.org /encyclopedia/GammaFunctionMultivariateComplex.html (79 words)

	Gamma function (Site not responding. Last check: 2007-11-06)
		In fact, the so-called Gamma function extends the definition of the factorial to the entire complex plane.
		A close relative to the Gamma function is the incomplete Gamma function.
		The incomplete Gamma function can also be used to approximate the value of the Gamma function itself, by selecting a suitable high integration limit x.
	algolist.manual.ru /maths/count_fast/gamma_function.php (1395 words)

	incomplete gamma function (Site not responding. Last check: 2007-11-06)
		(a,x) is a variation on the gamma function.
		It may be clear that this is the same function, apart from a constant.
		The incomplete gamma function and its inverse are used in statistics.
	www.2dcurves.com /gamma/gammagi.html (62 words)

	GNU Scientific Library -- Reference Manual
		If you are writing numerical functions in a program which also uses GSL code you may find it convenient to adopt the same error reporting conventions as in the library.
		This function splits the number x into its normalized fraction f and exponent e, such that x = f * 2^e and 0.5 <= f < 1.
		This function converts the divided-difference representation of a polynomial to a Taylor expansion.
	www.gnu.org /software/gsl/manual/gsl-ref.html (7698 words)

	Distributions (Site not responding. Last check: 2007-11-06)
		The function is symmetric about the mean, it gains its maximum value at the mean, the minimum value is at plus and minus infinity.
		The "standard" gamma function is often quoted as having B = 1.
		The Rician probability density function is derived as for the Rayleigh distribution by considering the in-phase and quadrature components.
	astronomy.swin.edu.au /~pbourke/analysis/distributions (901 words)

	Gamma and Related Functions - Special Functions - Math and Statistics Library for C# and VB.NET: BLAS, LAPACK, more
		The Gamma function, G(x) is a generalization of the factorial.
		The incomplete Beta function and the regularized Beta function have definitions that are analogous to the similarly named Gamma functions.
		The DiGamma function Psi(x) is the derivative of the logarithm of the Gamma function.
	www.extremeoptimization.com /Mathematics/UsersGuide/SpecialFunctions/GammaFunctions.aspx (428 words)

	[No title]
		In short, Gamma is also a probability; specifically, it is computed as the difference between the probability that the rank ordering of the two variables agree minus the probability that they disagree, divided by 1 minus the probability of ties.
		In generalized additive models, the linear function of the predictor values is replaced by an unspecified (non-parametric) function, obtained by applying a scatterplot smoother to the scatterplot of partial residuals (for the transformed dependent variable values).
		At a local or global minimum, the discrepancy function should be at the bottom of a "valley," where all first partial derivatives are zero, so the elements of the gradient should all be near to zero when a minimum is obtained.
	www.statsoft.com /textbook/glosf.html (3048 words)

	Factorial and Gamma Functions (Site not responding. Last check: 2007-11-06)
		function over the complex plane using the algorithm of Kuki, CACM algorithm 421.
		is the general function and may be called with a symbolic or numeric argument.
		function; and for complex numeric arguments, it uses the Kuki algorithm.
	starship.python.net /crew/mike/maxima/html/macref/node24.html (441 words)

	Gamma Function (Site not responding. Last check: 2007-11-06)
		The use of gamma functions in the calculation of organ perfusion functions for n...
		A Remarkable Monotonic Property of the Gamma Function...
		Paul Godfrey on the Lanczos Implementation of the Gamma Function - Numericana...
	www.scienceoxygen.com /math/222.html (116 words)

	gamma - the gamma function
		The gamma function is defined for all complex arguments apart from the singular points 0,-1,-2,...
		The logarithmic derivative of gamma is implemented by the digamma function
		For numerical x, the functional equation is used to shift the argument to the range 0 < x < 1.
	www.mupad.de /doc/30/eng/stdlib_gamma.html (348 words)

	The Gamma function in the Mac OS X 10.2 Math Library
		Q: There are a number of functions described in /usr/include/math.h that deal with the gamma function.
		function that approximates the Gamma function in its natural scale.
		The Mac OS 9 gamma function that approximates the Gamma function (depricated).
	developer.apple.com /qa/qa2001/qa1143.html (136 words)

	Gamma Function by Integration (Site not responding. Last check: 2007-11-06)
		In your program, call a gamma function, also from a mathematical subroutine library of your choice, and compare it to your integration as a double check.
		The above integral is called the gamma function, which is essentially a "factorial" with real arguments, having the unique recurrence property like the conventional integer-based factorial.
		The gamma function occurs frequently in higher mathematics, and most major mathematical packages come with this function already pre-defined, usually with very different more efficient algorithms.
	www.glue.umd.edu /~nsw/ench250/gamma.htm (167 words)

	The gamma Function
		The gamma function, developed by Euler (biography), is a continuous extension of the factorials.
		However, γ(s) is related to the zeta function ζ(s), which is itself defined as a series, so I hope it all hangs together.
		This is almost the gamma function, except we start integrating at c instead of 0.
	www.mathreference.com /lc-z,gamma.html (785 words)

	Complex Log Gamma Function
		The log gamma function is simply the natural logarithm of the above function.
		It is frequently used in computations instead of the complex gamma function because it is less subject to overflow problems.
		This syntax computes the complex component of the complex log gamma function.
	www.itl.nist.gov /div898/software/dataplot/refman2/auxillar/clngam.htm (290 words)

	Gamma Function
		The gamma function is defined by the following integral that shows up frequently in many pure and applied mathematical settings:
		Note that the gamma function with a negative argument is defined by utilizing the recursion formula explained in the next section.
		, and that is why the gamma function is also commonly referred to as the generalized factorial function.
	www.efunda.com /math/gamma/index.cfm (110 words)

	GNU Scientific Library -- Reference Manual: Gamma Function
		Further information on the Gamma function can be found in Abramowitz & Stegun, Chapter 6.
		These routines compute the logarithm of the Gamma function, \log(\Gamma(x)), subject to x not a being negative integer.
		This routine computes the sign of the gamma function and the logarithm its magnitude, subject to x not being a negative integer.
	www.dulug.duke.edu /~mstenner/free-docs/gsl-ref-1.0/gsl-ref_114.html (540 words)

	Gamma & Exponential Distns
		This activity introduces the Gamma function and distribution and shows how it is the parent of the exponential distribution which measures the time to the first occurrence and the time between occurrences in a Poisson process.
		This shows that the gamma function is a continuous extension to the factorial function.
		The last integral is 1 since it is the integral of the density function for a gamma random variable over its full range of values.
	www.saintmarys.edu /~psmith/345act22.html (658 words)

	Factorial and Gamma function (Site not responding. Last check: 2007-11-06)
		The factorial is a special case of the more general Gamma function which can be applied to any real (or complex) number.
		When the Gamma function is applied to the positive integers its relationship to factorials is as follows
		The gamma function of 0.5 is of pi
	astronomy.swin.edu.au /~pbourke/analysis/gammafcn (88 words)

	GNU Scientific Library -- Reference Manual - Gamma Function (Site not responding. Last check: 2007-11-06)
		These routines compute the Gamma function @math{\Gamma(x)}, subject to x not being a negative integer.
		These routines compute the logarithm of the Gamma function, @math{\log(\Gamma(x))}, subject to @math{x} not a being negative integer.
		This routine computes the sign of the gamma function and the logarithm its magnitude, subject to @math{x} not being a negative integer.
	www.math.utah.edu /software/gsl/gsl-ref_114.html (574 words)

Try your search on: Qwika (all wikis)