Results 11 to 20 of about 9,521 (292)

Integration of Hypergeometric Supertrigonometric Functions Using Generalized Hypergeometric Functions and its Applications

Journal of Institute of Science and Technology
This study explores the integration of hypergeometric supertrigonometric functions, with a particular focus on hypergeometric supersine and hypergeometric supercosine functions, by leveraging the properties and relationships of generalized hypergeometric functions.
Ganesh Bahadur Basnet, Narayan Prasad Pahari, Resham Prasad Paudel   +2 more
openaire   +2 more sources

Extensions of Bicomplex Hypergeometric Functions and Riemann–Liouville Fractional Calculus in Bicomplex Numbers

Fractal and Fractional
In this paper, we present novel advancements in the theory of bicomplex hypergeometric functions and their applications. We extend the hypergeometric function to bicomplex parameters, analyse its convergence region, and define its integral and derivative
Ahmed Bakhet, Mohamed Fathi, Mohammed Zakarya, Ghada AlNemer, Mohammed A. Saleem   +4 more
doaj   +2 more sources

EXTENDED GENERALIZED τ -GAUSS’ HYPERGEOMETRIC FUNCTIONS AND THEIR APPLICATIONS

South East Asian J. of Mathematics and Mathematical Sciences, 2022
In this article, by means of the extended beta function, we introduce new extension of the generalized τ -Gauss’ hypergeometric functions and present some new integral and series representations (including the one obtained by adopt- ing the well-known Ramanujan’s Master Theorem).
Chauhan, Bharti, Rai, Prakriti
openaire   +3 more sources

On Analytical Continuation of the Horn’s Hypergeometric Functions H₃ and Their Ratios

Axioms
This paper considers the Horn’s hypergeometric function H3, which is closely related to other hypergeometric functions and has various mathematical or physical applications.
Roman Dmytryshyn, Tamara Antonova, Sofiia Hladun   +2 more
doaj   +2 more sources

Evaluation of certain families of log-cosine integrals using hypergeometric function approach and applications [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, we provide the analytical solutions of the families of certain definite integrals: ∫₀^π xᵐ{ln(2cos(x/2)}ⁿ dx (m∈ℕ₀ and n∈ℕ), in terms of multiple hypergeometric functions of Kampe de Feriet having the arguments ±1 and Riemann zeta ...
Mohammad Idris Qureshi, Shakir Hussain Malik   +1 more
doaj   +2 more sources

Legendre Polynomial Expansions of Hypergeometric Functions with Applications

Journal of Mathematical Physics, 1970
The expansion of a class of hypergeometric functions in a series of Legendre polynomials is derived. The range of validity and the meaning to be attached to the sums is investigated. Several applications to the problem of the scattering of charged particles are presented.
J. T. Holdeman
openaire   +3 more sources

Extended Conformable K-Hypergeometric Function and Its Application

Advances in Mathematical Physics
The extended conformable k-hypergeometric function finds various applications in physics due to its ability to describe complex mathematical relationships arising in different physical scenarios. Here are a few instances of its uses in physics, including
Maham Abdul Qayyum, Aya Mohammed Dhiaa, Abid Mahboob, Muhammad Waheed Rasheed, Abdu Alameri   +4 more
doaj   +2 more sources

On properties and applications of (p,q)-extended τ-hypergeometric functions

Comptes Rendus. Mathématique, 2018
We introduce the ( p , q ) -extended τ -hypergeometric and confluent hypergeometric functions along with their integral ...
Parmar, Rakesh K., Pogány, Tibor K., Saxena, Ram K.   +2 more
openaire   +5 more sources

Exploring the Applications of Bicomplex Confluent Hypergeometric Functions in Fractional Calculus and Statistical Distributions

Journal of Mathematics
This paper introduces a special version of hypergeometric functions constructed within the bicomplex system, referred to as the bicomplex confluent hypergeometric functions (BCHFs). We highlight important properties, concentrating on their structure with
Mohra Zayed, Ahmed Bakhet, Shahid Hussain, Aya M. Mourad   +3 more
doaj   +2 more sources

Derivatives of continued fractions with applications to hypergeometric functions

Journal of Computational and Applied Mathematics, 1987
The purpose of the present paper is to illustrate the method on regular C-fraction expansions for certain hypergeometric functions. The emphasis is on developing the formulas needed. Numerical examples are indicated in some special cases.
Haakon Waadeland
exaly   +4 more sources