Analytic study and statistical enforcement of extended beta functions imposed by Mittag-Leffler and Hurwitz-Lerch Zeta functions.

Special Function Theory is used in many mathematical fields to model scientific progress, from theoretical to practical. This helps efficiently analyze the newly expanded Beta class of functions on a complicated domain. We use Mittag-Leffler and Hurwitz Lerch zeta (HLZ) kernels to produce the Beta function using the convolution tool.

Exact Bahadur Slope for combining independent tests in the case of the Pareto distribution.

In this paper, we compared the Exact Bahadur Slope (EBS) and the asymptotic relative efficiency of four combination methods for testing a single hypothesis against a one-sided alternative in the case of Pareto distribution when the number of tests tends to infinity. These methods combine the p-value of the corresponding test into one overall test. Fisher's, logistic, the sum of p-values, and inverse normal procedures are the four techniques used in our study.

Differential inequalities imposed by the extended hypergeometric function.

Recently, the generalized hypergeometric function is extended by utilizing the Beta function. Based on this type of function, we introduce a new operator in the open unit disk. The present article investigates some subordination and superordination results for certain normalized analytic functions in the open unit disk, which are acted upon by the generalized Noor integral operator.

Mathematical model for adaptive evolution of populations based on a complex domain.

A mutation is ultimately essential for adaptive evolution in all populations. It arises all the time, but is mostly fixed by enzymes. Further, most do consider that the evolution mechanism is by a natural assortment of variations in organisms in line for random variations in their DNA, and the suggestions for this are overwhelming.