Results 181 to 190 of about 821 (208)

On the order of starlikeness of the shifted Gauss hypergeometric function

Journal of Mathematical Analysis and Applications, 2007
We determine for several ranges of real parameters the order of starlikeness of the shifted Gauss hypergeometric function and we give some consequences of our results, in particular some mapping properties of the Carlson–Shaffer convolution ...
Küstner, Reinhold
exaly   +2 more sources

A simplification of Laplace’s method: Applications to the Gamma function and Gauss hypergeometric function

Journal of Approximation Theory, 2009
The main difficulties in the Laplace’s method of asymptotic expansions of integrals are originated by a change of variables. We propose a variant of the method which avoids that change of variables and simplifies the computations.
JOSÉ L Lopez
exaly   +2 more sources

Some of the next articles are maybe not open access.

Related searches:

On irrationality measures of the values of Gauss hypergeometric function

manuscripta mathematica, 1993
Sei \(F(z)\) die spezielle Gaußsche hypergeometrische Funktion \(\sum_{n\geq 0} ((b)_ n/ (c)_ n) z^ n\), wobei \((a)_ n:= a(a+1) \dots (a+n-1)\) für \(n\geq 0\) definiert und \(-c\neq 0,1,\dots\) vorausgesetzt sei. Sind nun \(b\), \(c\) rationale Parameter, so sind Irrationalität und lineare Unabhängigkeit von Werten von \(F\) an rationalen ...
Heimonen, Ari, Matala-aho, Tapani, Väänänen, Keijo   +2 more
openaire   +1 more source

Formula for the Product of Gauss Hypergeometric Functions and Applications

Journal of Mathematical Sciences, 2020
The \(\Gamma\)-series is defined by a lattice \(B \subset \mathbb Z^N\) and a fixed vector \(\gamma \subset \mathbb C^N\). This paper contains a formula for the product of two \(\Gamma\)-series in four variables, connected with the lattice \(B=\mathbb{Z}\langle(1,-1,-1,1)\rangle\). As a consequence of the formula for the product of \(\Gamma\)-series, a
openaire   +2 more sources

On the Computation of Gauss Hypergeometric Functions

The American Statistician, 2015
The pioneering study undertaken by Liang etal. in 2008 (Journal of the American Statistical Association, 103, 410-423) and the hundreds of papers citing that work make use of certain hypergeometric functions. Liang etal. and many others claim that the computation of the hypergeometric functions is difficult.
openaire   +1 more source

The Gauss Hypergeometric Ratio As a Positive Real Function

SIAM Journal on Mathematical Analysis, 1982
The Gauss continued fraction for the ratio of two hypergeometric functions is converted into an ordinary fraction (all partial numerators are 1) and simplifications occurring for particular relations between the parameters are discussed. In particular, a very simple expansion is obtained for the ratio ${E /K}$ of the complete elliptic integrals.
openaire   +2 more sources

Extension of Pochhammer symbol, generalized hypergeometric function and τ-Gauss hypergeometric function

Analysis
Abstract We introduce new extension of the extended Pochhammer symbol and gamma function by using the extended Mittag-Leffler function. We also present extension of the generalized hypergeometric function as well as some of their special cases by using this extended Pochhammer symbol.
Komal Singh Yadav, Bhagwat Sharan, Ashish Verma   +2 more
openaire   +1 more source

Fourier transform representation of the generalized hypergeometric functions with applications to the confluent and Gauss hypergeometric functions

Applied Mathematics and Computation, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mohammed H. Al-Lail, Asghar Qadir
openaire   +1 more source

Introduction: the Euler−Gauss Hypergeometric Function

2011
The binomial series \({(1 + x)}^{\alpha } ={ \sum \nolimits }_{n=0}^{\infty }\frac{\alpha (\alpha - 1)\cdots (\alpha - n + 1)} {n!} {x}^{n},\quad \vert x\vert < 1\) is the generating function of binomial coefficients \(\left (\begin{array}{*{10}c} \alpha \\ n \end{array} \right )=\frac{\alpha (\alpha - 1)\cdots (\alpha - n + 1)} {n!}.\)A hypergeometric
Kazuhiko Aomoto, Michitake Kita
openaire   +1 more source

Multiple orthogonal polynomials with respect to Gauss' hypergeometric function

Studies in Applied Mathematics, 2022
Helder Lima, Ana F Loureiro
exaly