Results 41 to 50 of about 27,869 (205)

New Extension of Beta Function and Its Applications

International Journal of Mathematics and Mathematical Sciences, 2018
In the present paper, new type of extension of classical beta function is introduced and its convergence is proved. Further it is used to introduce the extension of Gauss hypergeometric function and confluent hypergeometric functions. Then we study their
Mehar Chand, Hanaa Hachimi, Rekha Rani
doaj   +1 more source

A new generalization of confluent hypergeometric function and whittaker function

Boletim da Sociedade Paranaense de Matemática, 2018
In this article, we introduce a further generalizations of the confluent hypergeometric function and Whittaker function by introducing an extra parameter in the extended con uent hypergeometric function dened by Parmar [15].
Nabiullah Khan, Talha Usman, Mohd Ghayasuddin   +2 more
doaj   +1 more source

A highly accurate numerical method for solving boundary value problem of generalized Bagley‐Torvik equation

Mathematical Methods in the Applied Sciences, EarlyView.
A highly accurate numerical method is given for the solution of boundary value problem of generalized Bagley‐Torvik (BgT) equation with Caputo derivative of order 0<β<2$$ 0<\beta <2 $$ by using the collocation‐shooting method (C‐SM). The collocation solution is constructed in the space Sm+1(1)$$ {S}_{m+1}^{(1)} $$ as piecewise polynomials of degree at ...
Suzan Cival Buranay, Mtema James Chin, Nazim I. Mahmudov   +2 more
wiley   +1 more source

Fractional operators with generalized Mittag-Leffler k-function

Advances in Difference Equations, 2019
In this paper, our main aim is to deal with two integral transforms involving the Gauss hypergeometric functions as their kernels. We prove some composition formulas for such generalized fractional integrals with Mittag-Leffler k-function.
Shahid Mubeen, Rana Safdar Ali
doaj   +1 more source

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

Magnetic Resonance in Medicine, EarlyView.
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

Speed of Convergence to Normality When Regressors Are Nonstationary

Oxford Bulletin of Economics and Statistics, EarlyView.
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

Numerical evaluation of the Gauss hypergeometric function by power summations

Mathematics of Computation, 2014
. Numerical evaluation of the Gauss hypergeometric function 2 F 1 ( a,b ; c ; z ), with complex parameters a,b,c and complex argument z is no- toriously difficult. Carrying out the summation that defines the function may fail, even for moderate values of z .
J. Doornik
semanticscholar   +1 more source

A comparative study on generating function relations for generalized hypergeometric functions via generalized fractional operators

Advances in Difference Equations, 2018
In this paper, we present further generalizations of the beta function; Riemann–Liouville, Caputo and Kober–Erdelyi fractional operators by using confluent hypergeometric function with six parameters.
Ayşegül Çetinkaya, İ. Onur Kıymaz, Praveen Agarwal, Ravi Agarwal   +3 more
doaj   +1 more source

Small Sample Inference for Two‐Way Capture‐Recapture Experiments

International Statistical Review, Volume 93, Issue 1, Page 62-72, April 2025.
Summary The properties of the generalised Waring distribution defined on the non‐negative integers are reviewed. Formulas for its moments and its mode are given. A construction as a mixture of negative binomial distributions is also presented. Then we turn to the Petersen model for estimating the population size N in a two‐way capture‐recapture ...
Louis‐Paul Rivest, Mamadou Yauck
wiley   +1 more source

Classical Multiple Orthogonal Polynomials for Arbitrary Number of Weights and Their Explicit Representation

Studies in Applied Mathematics, Volume 154, Issue 3, March 2025.
ABSTRACT This paper delves into classical multiple orthogonal polynomials with an arbitrary number of weights, including Jacobi–Piñeiro, Laguerre of both first and second kinds, as well as multiple orthogonal Hermite polynomials. Novel explicit expressions for general recurrence coefficients, as well as the stepline case, are provided for all these ...
Amílcar Branquinho, Juan E. F. Díaz, Ana Foulquié‐Moreno, Manuel Mañas   +3 more
wiley   +1 more source