How do you write a Meijer function in Mathematica G?
How do you write a Meijer function in Mathematica G?
Definition of the Meijer G-function
- 0 ≤ m ≤ q and 0 ≤ n ≤ p, where m, n, p and q are integer numbers.
- ak − bj ≠ 1, 2, 3, for k = 1, 2., n and j = 1, 2., m, which implies that no pole of any Γ(bj − s), j = 1, 2., m, coincides with any pole of any Γ(1 − ak + s), k = 1, 2., n.
- z ≠ 0.
How do you write a Meijer G function in Matlab?
G p , q m , n ( a 1 , … , a p b 1 , … , b q | z ) = 1 2 π i ∫ ( ∏ j = 1 m Γ ( b j − s ) ) ( ∏ j = 1 n Γ ( 1 − a j + s ) ) ( ∏ j = m + 1 q Γ ( 1 − b j + s ) ) ( ∏ j = n + 1 p Γ ( a j − s ) ) z s d s .
What is gamma integration?
Using techniques of integration, it can be shown that Γ(1) = 1. Similarly, using a technique from calculus known as integration by parts, it can be proved that the gamma function has the following recursive property: if x > 0, then Γ(x + 1) = xΓ(x).
Why gamma function is used?
The gamma function then is defined as the analytic continuation of this integral function to a meromorphic function that is holomorphic in the whole complex plane except zero and the negative integers, where the function has simple poles….Gamma function.
| Gamma | |
|---|---|
| Fields of application | Calculus, mathematical analysis, statistics |
What is beta and gamma function?
Beta and gamma functions are popular functions in mathematics. Gamma is a single variable function while beta is a dual variable function. Beta function is used for computing and representing scattering amplitude for Regge trajectories. Also, it is applied in calculus using related gamma functions.
What is beta function used for?
In Physics and string approach, the beta function is used to compute and represent the scattering amplitude for Regge trajectories. Apart from these, you will find many applications in calculus using its related gamma function also.
What is the integral of the gamma function?
The Gamma function is defined by the integral below for. {\displaystyle \operatorname {Re} (z)>0.} is used to denote this function. the Gamma function is equal to the factorial function with its argument shifted by 1.
