Results 111 to 120 of about 4,179,714 (219)

Four Families of Summation Formulas for ₄F₃(1) with Application

Axioms
A collection of functions organized according to their indexing based on non-negative integers is grouped by the common factor of fixed integer N. This grouping results in a summation of N series, each consisting of functions partitioned according to ...
Belakavadi Radhakrishna Srivatsa Kumar, Arjun K. Rathie, Junesang Choi   +2 more
doaj   +1 more source

Series of convergence ratios “±427 $\frac{{\pm}4}{27}$ ” containing harmonic numbers

Demonstratio Mathematica
Three accelerating transformation formulae for hypergeometric series are systematically analyzed by the “coefficient extraction method”. Numerous harmonic series of convergence ratios “±427 $\frac{{\pm}4}{27}$ ” are evaluated in closed form, which fills ...
Li Chunli, Chu Wenchang
doaj   +1 more source

Application of Hypergeometric Distribution Series on Certain Subclass of Analytic Functions

International Journal of Analysis and Applications, 2016
The object of the present paper is to give some characterizations for hypergeometric distribution series to be in various subclasses of analytic functions.
Trailokya Panigrahi
doaj   +2 more sources

Congruences concerning truncated hypergeometric series

, 2017
We employ some formulae on hypergeometric series and p-adic Gamma function to establish several congruences.
Bing He
core   +1 more source

A New Closed-Form Formula of the Gauss Hypergeometric Function at Specific Arguments

Axioms
In this paper, the authors briefly review some closed-form formulas of the Gauss hypergeometric function at specific arguments, alternatively prove four of these formulas, newly extend a closed-form formula of the Gauss hypergeometric function at some ...
Yue-Wu Li, Feng Qi
doaj   +1 more source

Macdonald Polynomials and Multivariable Basic Hypergeometric Series

Symmetry, Integrability and Geometry: Methods and Applications, 2007
We study Macdonald polynomials from a basic hypergeometric series point of view. In particular, we show that the Pieri formula for Macdonald polynomials and its recently discovered inverse, a recursion formula for Macdonald polynomials, both represent ...
Michael J. Schlosser
doaj  

Algebraic Structures in Modular q-hypergeometric Series [PDF]

, 2012
We will discuss several questions related to q-hypergeometric series and modular functions. Nahm's conjecture is an attempt to answer the question of when a certain q-hypergeometric series can have modularity.
Lee, Chul-hee
core  

Uniform convergence of hypergeometric series

, 2006
Kyushu University 21st Century COE Program Development of Dynamic Mathematics with High Functionality九州大学21世紀COEプログラム「機能数理学の構築と展開」The considered problem is uniform convergence of sequences of hypergeometric series.
Vidunas, Raimundas
core  

Product formulas for basic hypergeometric series by evaluations of Askey-Wilson polynomials. [PDF]

Ramanujan J
Cohl HS, Schlosser MJ.
europepmc   +1 more source

Inversion of Bilateral Basic Hypergeometric Series

, 2003
We present a new matrix inverse with applications in the theory of bilateral basic hypergeometric series. Our matrix inversion result is directly extracted from an instance of Bailey's very-well-poised 6 # 6 summation theorem, and involves two ...
Michael Schlosser
core