Results 71 to 80 of about 395 (173)
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 +2 more
wiley +1 more source
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 +2 more
doaj +1 more source
Large parameter cases of the Gauss hypergeometric function
Journal of Computational and Applied Mathematics, 2003 21 pages, 4 ...
openaire +4 more sources
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
Certain Results on Extended Beta and Related Functions Using Matrix Arguments
Journal of New TheoryIn 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 +2 more
doaj +1 more source
Solution of abel‐type hypergeometric integral equation
Mathematical Modelling and Analysis, 1997 The paper is devoted to the study of the one‐dimensional integral equation involving the Gauss hypergeometric function in the kernel. The necessary and sufficient conditions for the solvability of such an equation in the space of summable functions are ...
A. A. Kilbas +3 more
doaj +1 more source
DARBOUX EVALUATIONS OF ALGEBRAIC GAUSS HYPERGEOMETRIC FUNCTIONS
Kyushu Journal of Mathematics, 2013 This paper presents explicit expressions for algebraic Gauss hypergeometric functions. We consider solutions of hypergeometric equations with the tetrahedral, octahedral and icosahedral monodromy groups. Conceptually, we pull-back such a hypergeometric equation onto its Darboux curve so that the pull-backed equation has a cyclic monodromy group ...
openaire +4 more sources
TRANSFORMATIONS AND INVARIANTS FOR DIHEDRAL GAUSS HYPERGEOMETRIC FUNCTIONS
Kyushu Journal of Mathematics, 2012 Hypergeometric equations with a dihedral monodromy group can be solved in terms of elementary functions. This paper gives explicit general expressions for quadratic monodromy invariants for these hypergeometric equations, using a generalization of Clausen's formula and terminating double hypergeometric sums.
openaire +3 more sources
Gauss quadrature approximations to hypergeometric and confluent hypergeometric functions
Journal of Computational and Applied Mathematics, 2002 The author analyzes the error of the Gauss quadrature formula to compute hypergeometric and confluent hypergeometric functions based on their integral representations. The error is analyzed both in terms of the derivatives of the integrand and in terms of the derivative-free contour integral representation of the remainder term in the case of the ...
openaire +1 more source
Potential of a Spheroid with Generalized Exponential Density Distribution
Open Astronomy, 2015 The internal potential of an inhomogeneous layered spheroid with a small ellipticity and general exponential density distribution is derived in an analytical form.
Kondratyev B. P., Kireeva E. N.
doaj +1 more source