Related papers: The Clausenian hypergeometric function $_3F_2$ wit…

The ability to obtain reliable point estimates of model parameters is of crucial importance in many fields of physics. This is often a difficult task given that the observed data can have a very high number of dimensions. In order to…

We develop an efficient and convergent numerical method for solving the inverse problem of determining the potential of nonlinear hyperbolic equations from lateral Cauchy data. In our numerical method we construct a sequence of linear…

The locally supersymmetric extension of the most general gravity theory in three dimensions leading to first order field equations for the vielbein and the spin connection is constructed. Apart from the Einstein-Hilbert term with…

We present a new methodology, suitable for implementation on computer, to perform the $\epsilon$-expansion of hypergeometric functions with linear $\epsilon$ dependent Pochhammer parameters in any number of variables. Our approach allows…

In this second of three introductory papers, we extend the notion of generalised Cesaro summation/convergence to the more natural setting of what we call remainder Cesaro summation/convergence. This greatly expands the range of problems…

In this article three expansion formulas for a generalized hypergeometric function $_4F_3$ are derived, when its upper parameters differ by integers. Though the results are special cases of a general continuation formula for $_pF_q$, they…

We find two-sided inequalities for the generalized hypergeometric function of the form ${_{q+1}}F_{q}(-x)$ with positive parameters restricted by certain additional conditions. Both lower and upper bounds agree with the value of…

We prove a new Bailey-type transformation relating WP-Bailey pairs. We then use this transformation to derive a number of new 3- and 4-term transformation formulae between basic hypergeometric series.

The authors survey recent results in special functions of classical analysis and geometric function theory, in particular the circular and hyperbolic functions, the gamma function, the elliptic integrals, the Gaussian hypergeometric…

In [Electron. J. Combin. 10 (2003), #R10], the author presented a new basic hypergeometric matrix inverse with applications to bilateral basic hypergeometric series. This matrix inversion result was directly extracted from an instance of…

The history of linear differential equations is over 350 years. By using Frobenius method and putting the power series expansion into linear differential equations, the recursive relation of coefficients starts to appear. There can be…

This is the first in a set of three papers providing an introduction to generalised Cesaro convergence. We start with traditional Cesaro methods for extending classical convergence and further generalise these to allow the calculation of…

In this article we find finite field analogues of certain product formulas satisfied by the classical hypergeometric series. We express product of two ${_2}F_1$-Gaussian hypergeometric series as ${_4}F_3$- and ${_3}F_2$-Gaussian…

For certain dimensionally-regulated one-, two- and three-loop diagrams, problems of constructing the epsilon-expansion and the analytic continuation of the results are studied. In some examples, an arbitrary term of the epsilon-expansion…

In the paper we study a special parameter containing algebraic inequality involving sum of reciprocals and product of positive real numbers whose sum is 1. We determine the best values of the parameter using a new optimization argument. In…

On the base of the distinction between covariant and contravariant metric tensor components, an approach from algebraic geometry will be proposed, aimed at finding new solutions of the Einstein's equations both in GTCCCM and in standard…

We calculate some infinite sums containing the digamma function in closed-form. These sums are related either to the incomplete beta function or to the Bessel functions. The calculations yield interesting new results as by-products, such as…

There are many instances known when the Fourier coefficients of modular forms are congruent to partial sums of hypergeometric series. In our previous work arXiv:1803.01830, such partial sums are related to the radial asymptotics of infinite…

The main object of this work is to show how some rather elementary techniques based upon certain inverse pairs of symbolic operators would lead us easily to several decomposition formulas associated with confluent hypergeometric functions…

We calculate some finite and infinite sums containing the digamma function in closed-form. For this purpose, we differentiate selected reduction formulas of the hypergeometric function with respect to the parameters applying some derivative…