Results 91 to 100 of about 5,448,308 (166)

On Askey’s extension of Clausen’s identity and its polynomial perturbation

Journal of Inequalities and Applications
The celebrated Clausen’s identity expresses the square of the Gauss hypergeometric series F 1 2 ( a , b ; a + b + 1 / 2 ; x ) ${}_{2}F_{1}(a,b;a+b+1/2;x)$ as a single hypergeometric F 2 3 ${}_{3}F_{2}$ series. Goursat showed in 1883 that replacing 1 / 2 $
Dmitrii Karp, Vinay Shukla
doaj   +1 more source

Bivariate generalization of the Gauss hypergeometric distribution

, 2014
: The bivariate generalization of the Gauss hypergeometric distribution is defined by the probability density function proportional to x α1−1y α2−1 (1 − x − y) β−1 (1 + ξ1x + ξ2y) −γ , x > 0, y > 0, x + y 0, i = 1, 2, β > 0, −∞ −1, i = 1, 2 are ...
Bedoya Valencia, Danilo, Nagar, Daya Krishna, Gupta, Arjun Kumar   +2 more
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Some Classes of Generating Relations Associated with a Family of the Generalized Gauss Type Hypergeometric Functions [PDF]

, 2015
In recent years, several interesting families of generating functions for various classes of hypergeometric and generalized hypergeometric functions in one, two and more variables were investigated systematically.
Lin, Shy-Der, M. Srivastava, H.
core  

Semi-orthogonal properties of a class of Gauss' hypergeometric polynomials

, 1993
We present three semi-orthogonal properties of a class of Gauss' hypergeometric polynomials.
Bajpai, S. D., S. D. Bajpai
core  

HypFun

, 2014
MATLAB code for computing the confluent and Gauss hypergeometric functions using a range of numerical ...
Pearson, John
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Sato-Tate distribution of <i>p</i>-adic hypergeometric functions. [PDF]

Res Number Theory, 2023
Pujahari S, Saikia N.
europepmc   +1 more source

On branched continued fraction expansions of hypergeometric functions \(F_M\) and their ratios

Modern Mathematical Methods
The paper investigates the problem of constructing branched continued fraction expansions of hypergeometric functions \(F_M(a_1,a_2,b_1,b_2;a_1,c_2;\mathbf{z})\) and their ratios.
Ivan Nyzhnyk, Roman Dmytryshyn, Tamara Antonova   +2 more
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Transformations of Gauss hypergeometric functions

The paper classifies algebraic transformations of Gauss hypergeometric functions and pull-back transformations between hypergeometric differential equations. This classification recovers the classical transformations of degree 2, 3, 4, 6, and finds other
Vidunas, Raimundas
core  

Hypergeometric functions in arithmetic geometry [PDF]

, 2009
textHypergeometric functions seem to be ubiquitous in mathematics. In this document, we present a couple of ways in which hypergeometric functions appear in arithmetic geometry.
Salerno, Adriana Julia, 1979-
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Probability density functions involving a generalized r–Gauss hypergeometric function

Le Matematiche, 2010
The aim of this paper is to study r–generalized gamma functions of a particular form.Moreover, we define a new probability density function (p.d.f) involving these new generalized functions.
Y. Ben Nakhi, S. L. Kalla
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