Special functions Gamma function and related functions Concept
Gamma function
Summary
The gamma function extends the factorial to real arguments. For it is an improper integral, and it satisfies for natural numbers . The node gamma function gives the precise definition.
Where this leads
56 pages build on this one.
- Beta function in terms of the gamma function
- Gauss's hypergeometric theorem
- Wilson polynomials
- Fermi–Dirac integral
- K-function
- Barnes integral
- Mehta integral
- Laguerre polynomials
- Fractional calculus
- Gamma function as Mellin transform of the exponential
- Dirichlet process
- Bessel–Clifford function
- Euler's integral representation of the hypergeometric function
- Riemann–Liouville fractional integral equation
- Cahen–Mellin integral
- Multiple gamma function
- Tautochrone problem
- Riemann–Liouville integral
- Riesz potential
- Poisson–Mellin–Newton cycle
- Caputo fractional derivative
- Meijer G-function
- Hilbert–Pólya conjecture
- Asymptotics of Bessel functions
- Appell series
- Dirichlet series as Mellin transforms
- Airy function
- Mittag-Leffler function
- Functional equation of the Riemann zeta function
- Lemniscate elliptic functions
- Coulomb wave function
- Digamma function
- Lauricella hypergeometric series
- Lindelöf hypothesis
- Dixon's identity
- Parabolic cylinder function
- Fractional differential equation
- Struve function
- Incomplete gamma function
- Dirichlet distribution
- Selberg integral
- Mellin transform of a theta series and the zeta function
- Fractional integration
- Abel inversion formula
- Bessel function of the first kind
- Lemniscate constant
- Riemann hypothesis
- Modified Bessel functions
- Tricomi confluent hypergeometric function
- Fox–Wright function
- Fox H-function
- q-gamma function
- Barnes G-function
- Multiplication theorem
- Riesz potential operator
- Ramanujan's master theorem
Further reading
- Web https://en.wikipedia.org/wiki/Gamma_function, lead section
About this page
| Tag | 0H5SYBSED9 |
|---|---|
| URI | m2://0H5SYBSED9 |
| Kind | concept |
| Writing | W1 stated |
| MSC | 33B15 |
| Same as |
Markdown · JSON · Edit on GitHub
What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Definitions
Results about this
- Beta function in terms of the gamma function
- Hankel contour integral for the gamma function
- Mehta integral
- Stirling's formula for the gamma function
- Weierstrass product for the gamma function
- Cahen–Mellin integral
- Log-convexity of the gamma function
- Legendre duplication formula
- Poles of the gamma function
- Selberg integral
- Hölder's theorem
- Euler–Gauss limit formula
- Gamma function has no zeros
- Wielandt's theorem
- Reflection formula for the gamma function
- Gamma of one half
- Gauss multiplication formula
- Multiplication theorem
- Euler integral for the gamma function
- Functional equation of the gamma function
- Holomorphy of the gamma function
Used by
- Beta function in terms of the gamma function
- Gauss's hypergeometric theorem
- Wilson polynomials
- Fermi–Dirac integral
- K-function
- Barnes integral
- Mehta integral
- Laguerre polynomials
- Fractional calculus
- Gamma function as Mellin transform of the exponential
- Bessel–Clifford function
- Euler's integral representation of the hypergeometric function
- Riemann–Liouville fractional integral equation
- Cahen–Mellin integral
- Multiple gamma function
- Riemann–Liouville integral
- Riesz potential
- Poisson–Mellin–Newton cycle
- Caputo fractional derivative
- Meijer G-function
- Asymptotics of Bessel functions
- Appell series
- Dirichlet series as Mellin transforms
- Airy function
- Mittag-Leffler function
- Functional equation of the Riemann zeta function
- Coulomb wave function
- Digamma function
- Lauricella hypergeometric series
- Dixon's identity
- Parabolic cylinder function
- Fractional differential equation
- Struve function
- Incomplete gamma function
- Dirichlet distribution
- Selberg integral
- Mellin transform of a theta series and the zeta function
- Fractional integration
- Abel inversion formula
- Bessel function of the first kind
- Lemniscate constant
- Modified Bessel functions
- Tricomi confluent hypergeometric function
- Fox–Wright function
- Fox H-function
- q-gamma function
- Barnes G-function
- Multiplication theorem
- Riesz potential operator
- Ramanujan's master theorem