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The extended conformable k-hypergeometric function finds various applications in physics due to its ability to describe complex mathematical relationships arising in different physical scenarios. Here are a few instances of its uses in physics, including nuclear physics, fluid dynamics, quantum mechanics, and astronomy. The main objectives of this paper are to introduce the extended conformable k-hypergeometric and confluent hypergeometric functions by utilizing the new definition of the α , k -beta function and studying its important properties, like integral representation, summation formula, derivative formula, transform formula, and generating function. Also, introduce the extension of the Riemann–Liouville fractional derivative and establish some results related to the newly defined fractional operator, such as the Mellin transform and relations to extended α , k -hypergeometric functions. [ABSTRACT FROM AUTHOR]

Agarwal et al. (2021) established the extension of several fundamental contiguous relations for G B . Our aim in this work is to investigate several properties of differentiation formulas, differential equations, recursion relations, differential recursion relations, confluence formulas, series representations, integration formulas, and infinite summations for Horn's hypergeometric function G B of three variables. Some well-known particular cases have additionally been given. [ABSTRACT FROM AUTHOR]

In this paper, we compute the reproducing kernel B m , α z , w for the generalized Fock space F m , α 2 ℂ . The usual Fock space is the case when m = 2. We express the reproducing kernel in terms of a suitable hypergeometric series 1 F q . In particular, we show that there is a close connection between B 4 , α z , w and the error function. We also obtain the closed forms of B m , α z , w when m = 1 , 2 / 3 , 1 / 2. Finally, we also prove that B m , α z , z ~ e α z m z m − 2 as ∣ z ∣ ⟶ ∞. [ABSTRACT FROM AUTHOR]

In this study, we derive recursion formulas for the Kampé de Fériet hypergeometric matrix function. We also obtain some finite matrix and infinite matrix summation formulas for the Kampé de Fériet hypergeometric matrix function. [ABSTRACT FROM AUTHOR]

In this paper, by using certain inverse pairs of symbolic operators introduced by Choi and Hasanov in 2011, we establish several decomposition formulas associated with the Gaussian triple hypergeometric functions. Some transformation formulas for these functions have also been obtained. [ABSTRACT FROM AUTHOR]

Sufficient conditions on a sequence {ak} of nonnegative numbers are obtained that ensures f(z) = ... akzk is starlike of nonnegative order in the unit disk. A result of Vietoris on trigonometric sums is extended in this pursuit. Conditions for close to convexity and convexity in the direction of the imaginary axis are also established. These results are applied to investigate the starlikeness of functions involving the Gaussian hypergeometric functions. [ABSTRACT FROM AUTHOR]

The effect of tilted harmonic excitation and parametric damping on the chaotic dynamics in an asymmetric magnetic pendulum is investigated in this paper. The Melnikov method is used to derive a criterion for transition to nonperiodic motion in terms of the Gauss hypergeometric function. The regular and fractal shapes of the basin of attraction are used to validate theMelnikov predictions. In the absence of parametric damping, the results showthat an increase of the tilt angle of the excitation causes the lower bound for chaotic domain to increase and produces a singularity at the vertical position of the excitation. It is also shown that the presence of parametric damping without a periodic fluctuation can enhance or suppress chaos while a parametric damping with a periodic fluctuation can increase the region of regular motions significantly. [ABSTRACT FROM AUTHOR]

The stress induced in a loaded beam will not exceed some threshold, but also its maximum deflection, as for all the elastic systems, will be controlled. Nevertheless, the linear beam theory fails to describe the large deflections; highly flexible linear elements, namely, rods, typically found in aerospace or oil applications, may experience large displacements-but small strains, for not leaving the field of linear elasticity-so that geometric nonlinearities become significant. In this article, we provide analytical solutions to large deflections problem of a straight, cantilevered rod under different coplanar loadings. Our researches are led by means of the elliptic integrals, but the main achievement concerns the Lauricella F D(3) hypergeometric functions use for solving elasticity problems. Each of our analytic solutions has been individually validated by comparison with other tools, so that it can be used in turn as a benchmark, that is, for testing other methods based on the finite elements approximation. [ABSTRACT FROM AUTHOR]

We investigate the Shintani functions attached to the spherical and nonspherical principal series representations of SL(3,R). We give the explicit formulas of the radial part of Shintani functions and evaluate the dimension of the space of Shintani functions. [ABSTRACT FROM AUTHOR]

We have obtained a new summation formula for 2ψ2 bilateral basic hypergeometric series by the method of parameter augmentation and demonstrated its various uses leading to some development of etafunctions, q-gamma, and q-beta function identities. [ABSTRACT FROM AUTHOR]

The authors define a new subclass of A of functions involving complex order in the open unit disk U. For this new class, we obtain certain inclusion properties involving the Gaussian hypergeometric functions. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to give some characterizations for a (Gaussian) hypergeometric function to be in various subclasses of starlike and convex functions. We also consider an integral operator related to the hypergeometric function. [ABSTRACT FROM AUTHOR]