Product of hypergeometric functions

Author: vzgo

August undefined, 2024

Webb11 sep. 2024 · Abstract: We consider a certain definite integral involving the product of two classical hypergeometric functions having complicated arguments. We show in this … Webb17 feb. 2009 · The later transform is a generalization of the discontinuous integral of Weber and Schafheitlin; in addition to reducing to other known integrals (for example, integrals involving products of powers, Bessel and Lommel functions), it contains numerous integrals of interest that are not readily available in the mathematical literature.

Singularities of hypergeometric functions in several variables

WebbThis book presents a geometric theory of complex analytic integrals representing hypergeometric functions of several variables. Starting from an integrand which is a product of powers of polynomials, integrals are explained, in an open affine space, as a pair of twisted de Rham cohomology and its dual over the coefficients of local system. Webb15 mars 1996 · Applying the principle of decomposition of a power series into an odd and an even part to a product of functions, many new products of two hypergeometric … hartland electrical

The Hypergeometric Functions (Chapter 2) - Special Functions

Webbstand out among other generalized hypergeometric functions by the power-law form of its Fourier transforms. Identities for inﬁnite series and integrals, which include these generalized hypergeometric functions, are proved. Keywords: Special functions, generalized hypergeometric function, fractional calculus 1 Introduction Webb15 nov. 2024 · The product of two hypergeometric functions with arguments xt and yt, respectively, is a power series in t. The coefficients are hypergeometric polynomials, … Webb5 maj 2013 · Just as Barnes's integral on the product of gamma functions was an analog of Gauss's 2 F 1 sum, these identities also have integral analogs and we discuss them. … hartland education support service center

Hypergeometric function - Encyclopedia of Mathematics

On Certain Linear, Bilinear and Bilateral Hypergeometric …

Webb13 apr. 2024 · The classical hypergeometric summation theorems have a significant role in the theory of generalized hypergeometric functions. Over the years generalization and extension of classical summation theorems for the series ${_{q+1}}F_q$, and their applications have been the predominant area of research.Notably, Masjed-Jamei and … WebbRecently, Brychkov et al. established several new and interesting reduction formulas for the Humbert functions (the confluent hypergeometric functions of two variables). The primary objective of this study was to provide an alternative and simple approach for proving four reduction formulas for the Humbert function ψ2. We construct intriguing series … hartland electrical malvernWebbThe singular hypersurface of any nonconﬂuent hypergeometric function has a solid amoeba. A hypergeometric function satisfying the Gelfand–Kapranov–Zelevinsky system of equations has singularities along the zero locus of the correspondingprincipalA-determinant (see [GKZ94]). Using Theorem 7 we arrive at the following corollary. hartland education

"Webb3 juli 2024 · The approach i am trying to follow begins by expressing each hypergeometric function in its infinite sum, resulting in a double sum, followed by Bailey's Transform. … " - Product of hypergeometric functions

Product of hypergeometric functions

Symmetry Free Full-Text Another Method for Proving Certain ...

Webb25 juni 2024 · $\begingroup$ First of all thank you for the answer and within it the wanted proof. Now I can be sure, that the formula is right but that was not what I desired. I have to reformulate my original question to clarify it : I would be really interested in a derivation of the formula, so that I can see how to get from the Mellin Integral of the Gaussian … WebbThe hypergeometric functions are solutions to the hypergeometric differential equation, which has a regular singular point at the origin. To derive the hypergeometric function from the hypergeometric differential equation (2) use the Frobenius method to reduce it to (3) … A formal extension of the hypergeometric function to two variables, resulting in four … Cayley, A. "On a Theorem Relating to Hypergeometric Series." Philos. Mag. 16, … See also Hypergeometric Function References Dumitriu, I.; Edelman, A.; and … for (Abramowitz and Stegun 1972, p. 505).. The confluent hypergeometric function of … This is the -hypergeometric function as defined by Bailey (1935), Slater (1966), … where is a hypergeometric function, is a generalized hypergeometric function, and … A transformation of a hypergeometric function, ... Clausen's product identity … References Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical …

Did you know?

Webb30 apr. 1991 · We study the connection opertors between the solutions with different asymptotics and show that they are given by products of elliptic theta functions. We prove that the connection operators automatically provide elliptic solutions of Yang-Baxter equations in the “face” formulation for any type of Lie algebra $$\mathfrak{g}$$ and … Webb7 nov. 2016 · Yes, there is a general result, via which this can be cast in terms of the 2 F 1 hypergeometric function. The relevant relation is formula 4.3. (12) on page 187 in " …

Webbhypergeometric functions based on contour integral representations. Such representations are important because they can be used for derivation of many relations between … Webb13 sep. 2024 · I am trying to solve definite integrals involving the product of confluent first order hypergeometric functions and rational functions as follows: Where p=0,1,2,3... When using the Matlab "integral" command the computation of these integrals takes a long time.

Webb23 nov. 2015 · This product of two Gaussian hypergeometric functions can be expressed by a sum over generalized hypergeometric functions 4 F 3 according to formula 4.3. (14) …

Webb6 feb. 2024 · In this research note, an interesting integral involving hypergeometric function has been evaluated in terms of gamma function. It is further used to evaluate an integral involving product of two ... charlies parkWebb23 jan. 2024 · Description. An Introduction to Hypergeometric, Supertigonometric, and Superhyperbolic Functions gives a basic introduction to the newly established hypergeometric, supertrigonometric, and superhyperbolic functions from the special functions viewpoint. The special functions, such as the Euler Gamma function, the Euler … charlies pawn and gun derby ksWebb1 jan. 2007 · Key wor ds and phrases: Product formulas, Gauss hypergeometric function, Jacobi polynomials, Jacobi functions, Bessel func- tions of the ﬁrst kind, Dirichlet … charlies pharmacy in mullens wvWebb27 juli 2024 · We prove a duality relation for the generalized basic hypergeometric functions. It forms a q-extension of a recent result of the second- and the third-named authors and generalizes both a q-hypergeometric identity due to the third-named author (jointly with Feng and Yang) and a recent identity for the Heine’s $${}_2\\phi _{1}$$ 2 ϕ 1 … hartland electricWebbI am looking for the product of Gaussian hypergeometric functions of the form 2 F 1 ( a, b; c; λ z) 2 F 1 ( d, e; f; ϕ z). I would like, but do not expect, an answer of the form p F q ( a, b; … charlie speed naceWebb5 maj 2013 · Just as Barnes's integral on the product of gamma functions was an analog of Gauss's 2 F 1 sum, these identities also have integral analogs and we discuss them. The hypergeometric identities provide a systematic approach to the evaluation of single sums of binomial coefficients. hartland electrical systems ltdWebb24 mars 2024 · The Meijer G-function is a very general function which reduces to simpler special functions in many common cases. The Meijer G-function is defined by (1) where … charlie spedding