Boyd shows in [3] that for a function with singularities in the imaginary plane, the Gegenbauer expansion of the function may have Runge-type oscillations so large that all hope of convergence for the method is lost. We consider the use of Padé-Gegenbauer interpolants to resolve these oscillations. We describe a fast interpolation-based reconstruction for computing the Padé-Gegenbauer approxima...

The contribution of the α3 single electron-loop vacuum-polarization diagrams to the Lamb shift of the muonic hydrogen has been evaluated recently by two methods. One uses the exact parametric representation of the vacuum-polarization function while the other relies on the Padé approximation method. High numerical precision of these calculations enables us to examine the accuracy of the Monte-Ca...

The equations governing the flow of an electrically conducting, incompressible viscous fluid over an infinite flat plate in the presence of a magnetic field are investigated using the homotopy perturbation method (HPM) with Padé approximants (PA) and 4 order Runge–Kutta method (4RKM). Approximate analytical and numerical solutions for the velocity field and heat transfer are obtained and compar...

This paper is devoted to the rational approximation of automatic real numbers, that is, real numbers whose expansion in an integer base can be generated by a finite automaton. We derive upper bounds for the irrationality exponent of famous automatic real numbers associated with the Thue–Morse, Rudin–Shapiro, paperfolding and Baum–Sweet sequences. These upper bounds arise from the construction o...

The equations governing the flow of an electrically conducting, incompressible viscous fluid over an infinite flat plate in the presence of a magnetic field are investigated using the homotopy perturbation method (HPM) with Padé approximants (PA) and 4 order Runge–Kutta method (4RKM). Approximate analytical and numerical solutions for the velocity field and heat transfer are obtained and compar...