21 papers · ranked by Valyu relevance
Petr Blaschke
We introduce a natural method of computing antiderivatives of a large class of functions (holomorphic near the origin) which stems from the observation that the series expansion of an antiderivative differs from the series expansion of the corresponding integrand by just two Pochhammer symbols. All antiderivatives are…
Faten F. Abdulnabi, Hiba F. Al-Janaby, Firas Ghanim
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…
Subuhi Khan, Ujair Ahmad, Mehnaz Haneef
The umbral methods are used to reformulate the theoretical framework of special functions and provide powerful techniques for uncovering new extensions and relationships among these functions. This research article introduces an innovative class of special polynomials, specifically the hypergeometric-Appell…
Markus Faulhuber
In this work we investigate the heat kernel of the Laplace-Beltrami operator on a rectangular torus and the according temperature distribution. We compute the minimum and the maximum of the temperature on rectangular tori of fixed area by means of Gauss’ hypergeometric function $_2F_1$ and the elliptic modulus. In…
Huda Al dweby, Maslina Darus
By making use of basic hypergeometric functions, a class of complex harmonic meromorphic functions with positive coefficients is introduced. We obtain some properties such as coefficient inequality, growth theorems, and extreme points.
Tie-Hong Zhao, Miao-Kun Wang, Wen Zhang, Yu-Ming Chu
In the article, we present several quadratic transformation inequalities for Gaussian hypergeometric function and find the analogs of duplication inequalities for the generalized Grötzsch ring function.
Charles F. Doran, Tyler L. Kelly, Adriana Salerno, Steven Sperber + 2 more
'John Voight' 'Ursula Whitcher'] We study the hypergeometric functions associated to five one-parameter deformations of Delsarte K3 quartic hypersurfaces in projective space. We compute all of their Picard-Fuchs differential equations; we count points using Gauss sums and rewrite this in terms of finite-field…
Subuhi Khan, Ujair Ahmad, Mehnaz Haneef
Mittag-Leffler functions Authors: ['Subuhi Khan' 'Ujair Ahmad' 'Mehnaz Haneef'] The umbral approach provides methods for comprehending and redefining special functions. This approach is employed efficiently in order to uncover intricacies and introduce new families of special functions. In this article, the umbral…
Kuldeep Singh Gehlot
In this paper we introduce the Two Parameter Gamma Function, Beta Function and Pochhammer Symbol. We named them, as p - k Gamma Function, p - k Beta Function and p - k Pochhammer Symbol and denoted as pΓk(x), pBk(x, y) and p(x)n,k respectively. We prove the several identities for pΓk(x), pBk(x, y) and p(x)n,k those…
Tiren Huang, Shenyang Tan, Xiaohui Zhang
We provide the monotonicity and convexity properties and sharp bounds for the generalized elliptic integrals \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}…
G. Dattoli, Mehnaz Haneef, Subuhi Khan, Silvia Licciardi
techniques Authors: ['G. Dattoli' 'Mehnaz Haneef' 'Subuhi Khan' 'Silvia Licciardi'] The umbral restyling of hypergeometric functions is shown to be a useful and efficient approach in simplifying the associated computational technicalities. In this article, the authors provide a general introduction to the umbral…
Enes Ata
In this paper, modified gamma and beta functions containing generalized M-series in their kernel are defined. Also, modified Gauss and confluent hypergeometric functions are defined using the modified beta function. Then, some properties of these modified special functions are obtained. Finally, the relationships…
Robert Reynolds, Hammad Khalil
By employing contour integration the derivation of a generalized double finite series involving the Hurwitz-Lerch zeta function is used to derive closed form formulae in terms of special functions. We use this procedure to find special cases of the summation and product formulae in terms of the Hurwitz-Lerch zeta…
Mumtaz Ahmad Khan, Shakeel Ahmed
This paper deals with the study of a generalized function of Mittag-Leffler type. Various properties including usual differentiation and integration, Euler(Beta) transforms, Laplace transforms, Whittaker transforms, generalized hypergeometric series form with their several special cases are obtained and relationship…
Dmitriy G. Seleznev, Alexander A. Prokin, Ekaterina M. Kurina
A methodology for identifying pairs of mutually associated and mutually incompatible species pairs based on qualitative ecological data in the ‘species-samples’ format is described. Statistical criteria for assessing the direction and strength of species associations using discrete hypergeometric and binomial…
Rui Fan, Qinghua Cui
Gene functional enrichment analysis represents one of the most popular bioinformatics methods for annotating the pathways and function categories of a given gene list. Current algorithms for enrichment computation such as Fisher’s exact test and hypergeometric test totally depend on the category count numbers of the…
Vladimir A. Kuznetsov, Andre Grageda, Davood Farbod
Modern high-throughput biological systems detection methods generate empirical frequency distributions (EFD) which exhibit complex forms and have long right-side tails. Such EFD are often observed in normal and pathological processes, of which the probabilistic properties are essential, but the underlying probability…
Authors not listed
Curried functions provide a systematic way of transforming multi-argument functions into nested singleargument functions. This transformation allows partial application and supports many central principles of functional programming. Their extension, called curried 𝑘-ary functions, naturally generalizes the familiar…
Eckhard Hitzer
– The Liouville theorem states that bounded holomorphic complex functions are necessarily constant. Holomorphic functions fulfill the socalled Cauchy-Riemann (CR) conditions. The CR conditions mean that a complex z-derivative is independent of the direction. Holomorphic functions are ideal for activation functions of…
Patrick Vallet
The influence of environmental factors on the dynamics of tree species can imply non-linear relationships. Some of them exhibit threshold effects. Hyperbolic functions effectively represent ecological processes that display threshold behaviours. However, the mathematical formulation of the hyperbola is complex, which…
Authors not listed
Hyperstructures and their hierarchical extensions [1]—SuperHyperStructures—provide a versatile formalism for modeling multi-layered and complex phenomena [2, 3]. A MicroStructure is a measurable mapping that assigns to each material point a single local state, representing attributes such as phase, crystal orientation…