The main contribution of this paper is to propose a closed expression for the Ramanujan constant alternating series, based on Euler–Boole summation formula. Such an not present in literature. We also highlight only choice parameter formula proposed by Hardy series positive terms, so value obtained as agrees with other methods divergent series. Additionally, we derive closed-formula chosen, unde...

The IBM Power4 processor uses series approximation to calculate square root. We formally verified the correctness of this algorithm using the ACL2(r) theorem prover. The proof requires the analysis of the approximation error on a Chebyshev series. This is done by proving Taylor’s theorem, and then analyzing the Chebyshev series using Taylor series. Taylor’s theorem is proved by way of non-stand...

In this study we produced a new method for solving regular differential equations with step size h and Taylor series. This method analyzes a regular differential equation with initial values and step size h. this types of equations include quadratic and cubic homogenous equations with constant coeffcients and cubic and second-level equations.

Via a unified geometric approach, class of generalized trigonometric functions with two parameters are analytically extended to maximal domains on which they univalent. Some consequences deduced concerning radius convergence for the Maclaurin series, commutation rotation, continuation beyond domain univalence, and periodicity.

This paper introduces a performance analysis tool for a wireless access point serving multiple mobile nodes. The channel conditions vary over time and the opportunistic scheduler in the access point can account for the channel conditions as well as for the number of backlogged packets for the different mobile nodes. The tool allows for fast and accurate calculations of the main performance meas...