Results 21 to 30 of about 302 (59)
Über die Anwendung des Tschebyschew-Verfahrens zum Ausbau des Weierstraß-Kerner-Verfahrens [PDF]
arXiv, 2023 We extend the Weierstrass-Kerner method by applying the Chebychev method to the function F that Kerner has used to show that the formula of Weierstrass actually is the Newton method applied to that F. The resulting method is already known but we want to present the process in one go and in a detailed way.
arxiv
An algorithm to approximate the real trilogarithm for a real argument [PDF]
arXiv, 2023 We present an algorithm to approximate the real trilogarithm for a real argument with IEEE 754-1985 double precision accuracy. The approximation is structured such that it can make use of instruction-level parallelism when executed on appropriate CPUs.
arxiv
Numerical evaluation of two and three parameter Mittag-Leffler functions
, 2015 The Mittag-Leffler (ML) function plays a fundamental role in fractional calculus but very few methods are available for its numerical evaluation. In this work we present a method for the efficient computation of the ML function based on the numerical ...
Garrappa, Roberto
core +2 more sources
Theta function identities and q series [PDF]
arXiv, 2023 We establish some functional identities of theta functions, an elementary proof of classical fourth-order identities, Landen transformations, and q series from the eigenvectors of the discrete Fourier transform. Also, we derive connection between Rogers-Ramanujan type identity and theta function identity.
arxiv
, 2007 This paper sketches a technique for improving the rate of convergence of a general oscillatory sequence, and then applies this series acceleration algorithm to the polylogarithm and the Hurwitz zeta function.
A. Jonquière +10 more
core +5 more sources
Algorithms for Evaluation of the Wright Function for the Real Arguments’ Values [PDF]
, 2008 2000 Math. Subject Classification: 33E12, 65D20, 33F05, 30E15The paper deals with analysis of several techniques and methods for the numerical evaluation of the Wright function.
Luchko, Yury
core
, 2014 Local iterated function systems are an important generalisation of the standard (global) iterated function systems (IFSs). For a particular class of mappings, their fixed points are the graphs of local fractal functions and these functions themselves are
Barnsley, Michael F. +2 more
core
Ramanujan type $1/π$ Approximation Formulas [PDF]
arXiv, 2011 In this article we use theoretical and numerical methods to evaluate in a closed-exact form the parameters of Ramanujan type $1/\pi$ formulas.
arxiv
Bends in the plane with variable curvature [PDF]
, 2017 Explicit formulae for planar variable curvature bends are constructed using Euler’s method of natural equations. The bend paths are expressed in terms of special functions.
Peters, Frank H., Sheehan, Robert N.
core
, 2017 We describe a method for the numerical evaluation of normalized versions of the associated Legendre functions $P_\nu^{-\mu}$ and $Q_\nu^{-\mu}$ of degrees $0 \leq \nu \leq 1,000,000$ and orders $-\nu \leq \mu \leq \nu$ on the interval $(-1,1)$.
Bremer, James
core +1 more source