17 papers · ranked by Valyu relevance
Florian Fürnsinn, Sergey Yurkevich
We provide a complete classification of the algebraicity of (generalized) hypergeometric functions with no restriction on the set of their parameters. Our characterization relies on the interlacing criteria of Christol (1987) and Beukers-Heckman (1989) for globally bounded and algebraic hypergeometric functions…
B. Ananthanarayan, Souvik Bera, Samuel Friot, Tanay Pathak
We present the Olsson.wl Mathematica package which aims to find linear transformations for some classes of multivariable hypergeometric functions. It is based on a well-known method developed by P. O. M. Olsson in J. Math. Phys. 5, 420 (1964) in order to derive the analytic continuations of the Appell F1 double…
W. N. Mathews, M. A. Esrick, Zu Yao Teoh, J. K. Freericks
The confluent hypergeometric equation, also known as Kummer's equation, is one of the most important differential equations in physics, chemistry, and engineering. Its two power series solutions are the Kummer function, 𝑀(𝑎, 𝑏, 𝑧), often referred to as the confluent hypergeometric function of the first kind, and…
Paweł J. Szabłowski
We find some identities involving the Pochhammer symbol (rising factorial) and apply them to find a closed form for some integrals of the Jacobi polynomials, as well as a hypergeometric function multiplied by the product of the Jacobi polynomial and the Beta density that makes this polynomial a member of the family of…
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…
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…
Snehasis Bera, Sourav Das, Abhijit Banerjee
In this work, generalized hypergeometric functions for bicomplex argument is introduced and its convergence criteria is derived. Furthermore, integral representation of this function has been established. Moreover, quadratic transformation, differential relation, analyticity and contiguous relations of this function…
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…
Rahul J. Jada, Meera H. Chudasama
In this paper, new generalizations of the hyper Bessel type differential operator called it as $\ell$-H derivative operator, are studied, and using these, some of the classical results of calculus are extended. Also, new generalization of a natural number is defined and then its combinatorial properties are extended.…
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…
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…
Howard S. Cohl, Michael J. Schlosser
We review and derive transformation and summation formulas for bilateral basic hypergeometric series. Our study focuses on consequences of certain bilateral extensions of two important results by Bailey, namely a transformation for very-well-poised $_8\!W_7$ series in terms of two balanced $_4\phi _3$ series, and a…
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…
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…
Daniele Dall’Olio, Eric Sträng, Amin T Turki, Jesse M Tettero + 12 more
Onco-hematological studies are increasingly adopting statistical mixture models to support the advancement of the genetically-driven classification systems for blood cancer. Targeting enhanced patients stratification based on the sole role of molecular biology attracted much interest and contributes to bring…
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…