Results 171 to 180 of about 3,001,317 (197)

Inequalities for the Gaussian hypergeometric function

Science China Mathematics, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yuming Chu
exaly   +3 more sources

Monotonicity of three kinds of functions involving the Gaussian hypergeometric function

Bulletin of the Belgian Mathematical Society - Simon Stevin, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jing-Feng Tian
exaly   +2 more sources

Landen inequalities for Gaussian hypergeometric function

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2021
The paper contains several Landen inequalities, and quadratic and cubic transformation inequalities for the general Gaussian hypergeometric function \(_2F_1(a, b; c ;x)\). The authors present Landen inequalities and other Ramanujan's quadratic, cubic transformation inequalities for the Gaussian hypergeometric function \(F(a,b;c;r)\) which are ...
Tie-Hong Zhao, Miao-Kun Wang, Guo-Jing Hai, Yu-Ming Chu   +3 more
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Starlikeness of Gaussian Hypergeometric Functions Using Positivity Techniques

Bulletin of the Malaysian Mathematical Sciences Society, 2016
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Priyanka Sangal, A. Swaminathan
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On the Absolute Monotonicity of the Logarithmic of Gaussian Hypergeometric Function

Bulletin of the Iranian Mathematical Society
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Jiahui Wu, Tiehong Zhao
openaire   +1 more source

Monotonicity of the ratio of two arbitrary gaussian hypergeometric functions

Mathematica Slovaca
Abstract The Gaussian hypergeometric function is an important class of special functions, whose mathematical properties have long been of interest to the academic community. In this paper, by utilizing monotonicity rules, we establish the necessary and sufficient conditions for the monotonicity of the ratio of two Gaussian hypergeometric
Mao, Zhong-Xuan, Tian, Jing-Feng
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DEVELOPMENT OF A GAUSSIAN HYPERGEOMETRIC FUNCTION CODE IN COMPLEX DOMAINS

International Journal of Modern Physics C, 1993
The analytic properties of the Gaussian hypergeometric function is reviewed and applied to the development of a Fortran function code. The code developed can be used to evaluate the hypergeometric function on the whole complex plane with arbitrary complex parametric values.
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Triple Gaussian hypergeometric functions. I

1994
The author studies second order solution types of the systems of hypergeometric functions \(F_ G\) and \(F_ T\) of three variables introduced by \textit{G. Lauricella} [Rend. Circ. Mat. Palermo 7, 111-158 (1893)] and \textit{S. Saran} [Ganita 5, No. 2, 77-91 (1954; Zbl 0058.296)] and shows that the partial differential equations associated with the ...
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Parameter derivatives of the jacoby polynomials and the gaussian hypergeometric function

Integral Transforms and Special Functions, 1994
The paper's main result is a simple derivation rule for the Jacobi polynomials with respect to their parameters, i.e. for [image omitted] . It is obtained via relations for the Guassian hypergeometric function concernuing parameter derivatives and integer shifts in the first two arguments.
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A Gaussian Hypergeometric Function Identity

SIAM Review, 1977
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