We describe a class of geometric objects called k-omino towers that are created by stacking blocks of size k×1×1 on a convex base composed of these same k-omino blocks. These towers are equivalent to a class of fixed polyominoes or lattice animals, through the creation of a polyomino using the boundary of the two-dimensional vertical face of the tower. By applying a partition to the set of k-om...

Three- and four-term recurrence relations for hypergeometric functions of the second order (such as Appell, Horn, etc.) are starting point constructing branched continued fraction expansions ratios these functions. These essential obtaining simplest structure fractions (elements which simple polynomials) approximating solutions systems partial differential equations, well some analytical two va...

The Gauss hypergeometric distribution with the density proportional to xα−1 (1− x)β−1 (1 + ξx)−γ , 0 < x < 1 arises in connection with the priori distribution of the parameter ρ (0 < ρ < 1) representing traffic intensity in a M/M/1 queue system. In this article, we define and study a multivariate generalization of this distribution and derive some of its properties like marginal densities, join...

The focus of this research is to use a new extended beta function and develop the extensions Gauss hypergeometric functions confluent formulas that are presumed be new. Four theorems have also been defined under generalized fractional integral operators provide an image formula for extension functions. Moreover, discussed analogous statements in terms Weyl, Riemann–Liouville, Erdélyi–Kober, Sai...

We will consider nonlinear holonomy effects -especially the spin dissipation dynamicsarising in the transport of a linear rotator between metric spaces with different curvature (positive, zero, negative). The extra 3D spin vector current induced by curvature or metric distortion provides for a holonomic attractor called ”Magic Angle Precession” (MAP). Limitations and instabilities of the spin c...

We prove the following theorems: 1) The Laurent expansions in ε of the Gauss hypergeometric functions 2F1(I1 + aε, I2 + bε; I3 + p q + cε; z), 2F1(I1 + p q + aε, I2 + p q + bε; I3+ p q + cε; z) and 2F1(I1+ p q +aε, I2+ bε; I3 + p q + cε; z), where I1, I2, I3, p, q are arbitrary integers, a, b, c are arbitrary numbers and ε is an infinitesimal parameter, are expressible in terms of multiple poly...