The Dirichlet distribution is a well-known candidate in modeling compositional data sets. However, the presence of outliers, fails to model such sets, making other extensions necessary. In this paper, Kummer–Dirichlet and gamma are coupled, using beta-generating technique. This development results proposal distribution, which presents greater flexibility Some general properties, as probability ...

As of late, the study Fractional Calculus (FC) and Special Functions (SFs) has been interestingly prompted in various realms mathematics, engineering sciences. This is due to considerable demonstrated potential their applications. Among these SFs, Gamma function Mittag-Leffler functions are most renowned distinguished. Numerous authors continue this line. The current analysis attempts introduce...

The hypergeometric zeta function is defined in terms of the zeros of the Kummer function M(a, a+b; z). It is established that this function is an entire function of order 1. The classical factorization theorem of Hadamard gives an expression as an infinite product. This provides linear and quadratic recurrences for the hypergeometric zeta function. A family of associated polynomials is characte...

Kummer type formulas are identities of hypergeometric series. A symmetry by the permutations of n-letters yields these formulas. We will present an algorithmic method to derive known and new Kummer type formulas. The algorithm utilizes several algorithms in algebra and geometry for generating Kummer type formulas.

This paper describes, in detail, a process for constructing Kummer K3 surfaces, and other “generalized” Kummer K3 surfaces. In particular, we look at how some well-known geometrical objects such as the platonic solids and regular polygons can inspire the creation of singular surfaces, and we investigate the resolution of those surfaces. Furthermore, we will extend this methodology to examine th...

In the first part of this paper we give a survey of classical results on Kummer surfaces with Picard number 17 from the point of view of lattice theory. We prove ampleness properties for certain divisors on Kummer surfaces and we use them to describe projective models of Kummer surfaces of (1, d)polarized Abelian surfaces for d = 1, 2, 3. As a consequence we prove that in these cases the Néron–...