#Line integral wolfram mathematica pro

2 Relationship between the G-function and the generalized hypergeometric function Logic Pro MATLAB Adobe Photoshop 2020 Autodesk Maya Wolfram Mathematica.

One application of the Meijer G-function has been the particle spectrum of radiation from an inertial horizon in the moving mirror model of the dynamical Casimir effect ( Good 2020). The machine itself is capable of doing all of the intermediary steps: partial derivatives, dot products, and cross products. Instead of calculating all of the individual pieces by hand, I am going to plug everything into an integral.

The process will look much like a line integral.

G 2( dx δ) of two G-functions with rational γ/ δ equals just another G-function, and generalizations of integral transforms like the Hankel transform and the Laplace transform and their inverses result when suitable G-function pairs are employed as transform kernels.Ī still more general function, which introduces additional parameters into Meijer's G-function, is Fox's H-function and is used for Matrix transform by Ram Kishore Saxena We are now ready to calculate a surface integral.

For example, the definite integral over the positive real axis of any function g( x) that can be written as a product G 1( cx γ) The wide coverage of special functions also lends power to uses of Meijer's G-function other than the representation and manipulation of derivatives and antiderivatives. In combination with a functional equation that allows to liberate from a G-function G( z) any factor z ρ that is a constant power of its argument z, the closure implies that whenever a function is expressible as a G-function of a constant multiple of some constant power of the function argument, f( x) = G( cx γ), the derivative and the antiderivative of this function are expressible so too. A notable property is the closure of the set of all G-functions not only under differentiation but also under indefinite integration. With the modern definition, the majority of the established special functions can be represented in terms of the Meijer G-function.

#Line integral wolfram mathematica full

The first definition was made by Meijer using a series nowadays the accepted and more general definition is via a line integral in the complex plane, introduced in its full generality by Arthur Erdélyi in 1953. This was not the only attempt of its kind: the generalized hypergeometric function and the MacRobert E-function had the same aim, but Meijer's G-function was able to include those as particular cases as well. In mathematics, the G-function was introduced by Cornelis Simon Meijer ( 1936) as a very general function intended to include most of the known special functions as particular cases. and a complete programming hunt for, , many linear environment.

Plot of the Meiger G function G(((a 1.,a n),(a n+1.,a p)),((b 1.,b m),(b m+1.,b q)),z) input ((½),()),((⅓),()) in the complex plane from -2-2i to 2+2i 11 MATHEMATICA To WOLFRAM RESEARCH An Extraordinarily Powerful, Mathematica is the.