Approximate closed-form formulas for the zeros of the Bessel Polynomials [PDF]
, 2011 We find approximate expressions x(k,n) and y(k,n) for the real and imaginary parts of the kth zero z_k=x_k+i y_k of the Bessel polynomial y_n(x). To obtain these closed-form formulas we use the fact that the points of well-defined curves in the complex ...
Calderon, Marisol L., Campos, Rafael G.
core +3 more sources
An advanced variant of an interpolatory graphical display algorithm [PDF]
, 2004 In this paper an advanced interpolatory graphical display algorithm based on cardinal B-spline functions is provided. It is well-known that B-spline functions are a flexible tool to design various scale rapresentations of a signal.
ALA, Guido +4 more
core +2 more sources
A matrix-algebraic algorithm for the Riemannian logarithm on the Stiefel manifold under the canonical metric [PDF]
, 2017 We derive a numerical algorithm for evaluating the Riemannian logarithm on the Stiefel manifold with respect to the canonical metric. In contrast to the existing optimization-based approach, we work from a purely matrix-algebraic perspective.
Zimmermann, Ralf
core +2 more sources
Expansion formulas in terms of integer-order derivatives for the Hadamard fractional integral and derivative [PDF]
, 2011 We obtain series expansion formulas for the Hadamard fractional integral and fractional derivative of a smooth function. When considering finite sums only, an upper bound for the error is given.
Almeida, R. +2 more
core +4 more sources
Fractional order optimal control problems with free terminal time [PDF]
, 2013 We consider fractional order optimal control problems in which the dynamic control system involves integer and fractional order derivatives and the terminal time is free.
A. A. Kilbas +23 more
core +2 more sources
Computation of the entropy of polynomials orthogonal on an interval. [PDF]
, 2004 We give an effective method to compute the entropy for polynomials orthogonal on a segment of the real axis that uses as input data only the coefficients of the recurrence relation satisfied by these polynomials.
A. Martínez-Finkelshtein +15 more
core +3 more sources
, 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
Some new series for $1/\pi$ and related congruences [PDF]
, 2016 In this paper we prove some new series for $1/\pi$ as well as related congruences. We also raise several new kinds of series for $1/\pi$ and present some related conjectural congruences involving representations of primes by binary quadratic forms ...
Sun, Zhi-Wei
core
Computing the Gamma function using contour integrals and rational approximations [PDF]
, 2005 Some of the best methods for computing the gamma function are based on numerical evaluation of Hankel's contour integral. For example, Temme evaluates this integral based on steepest-decent contours by the trapezoid rule.
Schmelzer, Thomas, Trefethen, Lloyd N.
core
Accurate and efficient computation of nonlocal potentials based on Gaussian-sum approximation
, 2015 We introduce an accurate and efficient method for a class of nonlocal potential evaluations with free boundary condition, including the 3D/2D Coulomb, 2D Poisson and 3D dipolar potentials.
Exl, Lukas +2 more
core +2 more sources