19 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…
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…
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…
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.
Duriye Korkmaz Duzgun, Esra Erkuş-Duman
Z − 0 denotes the set of nonpositive integers, and Γ(λ) is gamma function. In (1.1), the absence of parameters p or q is emphasized by a dash (interpreting an empty product as 1). For example, if no numerator or denominator parameters are present, i.e., p = q = 0, the result is 0F0 (−; −; z) = P∞ n=0 z n n! similarly…
Mohammad Idris Qureshi, Saima Jabee, Mohammad Shadab
Motivated by the substantial development of the special functions, we contribute to establish some rigorous results on the general series identities with bounded sequences and hypergeometric functions with different arguments, which are generally applicable in nature. For the application purpose, we apply our results…
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…
Tuhtasin Ergashev
The main object of this work is to show how some rather elementary techniques based upon certain inverse pairs of symbolic operators would lead us easily to several decomposition formulas associated with confluent hypergeometric functions of two and more variables. Many operator identities involving these pairs of…
E.G. Abramochkin, E.V. Razueva
Recently, a two-dimensional light field that is a product of three Airy functions with linear arguments has been proposed and invesigated in [15]. It has been shown that the Fourier image of this three-Airy beam has a radially symmetric intensity with a super-Gaussian decrease. Three-Airy beams, Airy wavelets in two…
Howard S. Cohl, Roberto S. Costas-Santos, Linus Ge
In this survey paper, we exhaustively explore the terminating basic hypergeometric representations of the Askey-Wilson polynomials and the corresponding terminating basic hypergeometric transformations that these polynomials satisfy.
Sudhir Pujahari, Neelam Saikia
Recently Ono, Saad and the second author [21] initiated a study of value distribution of certain families of Gaussian hypergeometric functions over large finite fields. They investigated two families of Gaussian hypergeometric functions and showed that they satisfy semicircular and Batman distributions. Motivated by…
Howard S. Cohl, Roberto S. Costas-Santos, Tanay V. Wakhare
Demonstrating the striking symmetry between calculus and q-calculus, we obtain q-analogues of the Bateman, Pasternack, Sylvester, and Cesàro polynomials. Using these, we also obtain q-analogues for some of their generating functions. Our q-generating functions are given in terms of the basic hypergeometric series 4ϕ5…
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…
Howard S. Cohl, Sean J. Nair, Rebekah M. Palmer
In Cohl (2012) [1], orthogonality and Hankel's transform are used to generate solutions to new definite integrals based on known integrals. In this paper, we use the method of integral transforms to create new integrals from a variety of known integrals containing Bessel functions of the first kind Jν . In this method…
Sean K. Martin, John P. Aggleton, Shane M. O’Mara
Large-scale simultaneous in vivo recordings of neurons in multiple brain regions raises the question of the probability of recording direct interactions of neurons within, and between, multiple brain regions. In turn, identifying inter-regional communication rules between neurons during behavioural tasks might be…
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…
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…
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…
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…