Results 81 to 90 of about 821 (208)

Parametric Transformations between the Heun and Gauss Hypergeometric Functions

Funkcialaj Ekvacioj, 2013
The hypergeometric and Heun functions are classical special functions. Transformation formulas between them are commonly induced by pull-back transformations of their differential equations, with respect to some coverings P1-to-P1. This gives expressions of Heun functions in terms of better understood hypergeometric functions. This article presents the
Vidunas, R., Filipuk, G.
openaire   +4 more sources

Exact analytical solutions of the Bloch equation for the hyperbolic‐secant and chirp pulses

Magnetic Resonance in Medicine, Volume 94, Issue 5, Page 2140-2149, November 2025.
Abstract Purpose To improve the accuracy and generality of analytical solutions of the Bloch equation for the hyperbolic‐secant (HS1) and chirp pulses in order to facilitate application to truncated and composite pulses and use in quantitative methods.
Ryan H. B. Smith, Donald Garwood, Michael Garwood   +2 more
wiley   +1 more source

On a problem for mixed type equation with partial riemann-liouville fractional derivative

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2016
The uniqueness and existence of solutions of a nonlocal problem proved for an equation of mixed type. This equation contains diffusion equation of fractional order.
Oleg A Repin, Anna V Tarasenko
doaj   +1 more source

Speed of Convergence to Normality When Regressors Are Nonstationary

Oxford Bulletin of Economics and Statistics, Volume 87, Issue 5, Page 871-879, October 2025.
ABSTRACT Stochastic and deterministic trends always coexist in data generating processes, which causes the nonstationarity and non‐standard distributions of statistics used in inference. It is known that the presence of the deterministic trend leads to asymptotic normality of the t‐statistics.
Lukasz T. Gatarek, Aleksander Welfe
wiley   +1 more source

Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions

, 2023
In the paper, by virtue of the binomial inversion formula, a general formula of higher order derivatives for a ratio of two differentiable function, and other techniques, the authors compute several sums in terms of the beta function and its partial ...
Feng Qi (祁锋), Chuan-Jun Huang
core   +1 more source

Expansions of the Solutions of the General Heun Equation Governed by Two-Term Recurrence Relations for Coefficients

Advances in High Energy Physics, 2018
We examine the expansions of the solutions of the general Heun equation in terms of the Gauss hypergeometric functions. We present several expansions using functions, the forms of which differ from those applied before.
T. A. Ishkhanyan, T. A. Shahverdyan, A. M. Ishkhanyan   +2 more
doaj   +1 more source

Jaccard dissimilarity in stochastic community models based on the species‐independence assumption

Ecography, Volume 2025, Issue 8, August 2025.
A fundamental problem in ecology is understanding the changes in species composition among sites (i.e. beta‐diversity). It is unclear how spatial heterogeneity in species occupancy across sites shapes patterns of beta‐diversity. To address this question, we develop probabilistic models that consider two spatial or temporal sites, where presence ...
Ryosuke Iritani, Vicente J. Ontiveros, David Alonso, José A. Capitán, William Godsoe, Shinichi Tatsumi   +5 more
wiley   +1 more source

A Class of Extended Fractional Derivative Operators and Associated Generating Relations Involving Hypergeometric Functions

Axioms, 2012
Recently, an extended operator of fractional derivative related to a generalized Beta function was used in order to obtain some generating relations involving the extended hypergeometric functions [1].
H. M. Srivastava, Rakesh K. Parmar, Purnima Chopra   +2 more
doaj   +1 more source

Principal frequency of clamped plates on RCD(0,N)${\sf RCD}(0,N)$ spaces: Sharpness, rigidity, and stability

Proceedings of the London Mathematical Society, Volume 131, Issue 2, August 2025.
Abstract We study fine properties of the principal frequency of clamped plates in the (possibly singular) setting of metric measure spaces verifying the RCD(0,N)${\sf RCD}(0,N)$ condition, that is, infinitesimally Hilbertian spaces with nonnegative Ricci curvature and dimension bounded above by N>1$N>1$ in the synthetic sense.
Alexandru Kristály, Andrea Mondino
wiley   +1 more source

Certain Results on Extended Beta and Related Functions Using Matrix Arguments

Journal of New Theory
In this study, we present and explore extended beta matrix functions (EBMFs) and their key properties. By utilizing the beta matrix function (BMF), we introduce novel extensions of the Gauss hypergeometric matrix function (GHMF) and Kummer hypergeometric
Saddam Husain, Rakibul Sk, Nabiullah Khan   +2 more
doaj   +1 more source