Results 41 to 50 of about 302 (59)

Numerical Computation of \prod_{n=1}^\infty (1 - tx^n) [PDF]

arXiv, 2002
I present and analyze a quadratically convergent algorithm for computing the infinite product \prod_{n=1}^\infty (1 - tx^n) for arbitrary complex t and x satisfying |x| < 1, based on the identity \prod_{n=1}^\infty (1 - tx^n) = \sum_{m=0}^\infty {(-t)^m x^{m(m+1)/2} \over (1-x)(1-x^2) ... (1-x^m)} due to Euler.
arxiv  

Study of the parametric effect of the wave profiles of the time-space fractional soliton neuron model equation arising in the topic of neuroscience

Partial Differential Equations in Applied Mathematics
Time-space fractional nonlinear problems (T-SFNLPs) play a crucial role in the study of nonlinear wave propagation. Time-space nonlinearity is prevalent across various fields of applied science, nonlinear dynamics, mathematical physics, and engineering ...
Md. Nur Alam, Md. Azizur Rahman
doaj  

One method for proving inequalities by computer [PDF]

arXiv, 2006
In this article we consider a method for proving a class of analytical inequalities via minimax rational approximations. All numerical calculations in this paper are given by Maple computer program.
arxiv  

Approximation of Askey-Wilson roots [PDF]

arXiv
This note presents a fixed-point formula designed to approximate the roots of Askey-Wilson poynomials for small parameter values.
arxiv  

Series of Reciprocal Powers of k-almost Primes [PDF]

arXiv, 2008
Sums over inverse s-th powers of semiprimes and k-almost primes are transformed into sums over products of powers of ordinary prime zeta functions. Multinomial coefficients known from the cycle decomposition of permutation groups play the role of expansion coefficients.
arxiv  

Enumeration of integral tetrahedra [PDF]

arXiv, 2008
We determine the numbers of integral tetrahedra with diameter $d$ up to isomorphism for all $d\le 1000$ via computer enumeration. Therefore we give an algorithm that enumerates the integral tetrahedra with diameter at most $d$ in $O(d^5)$ time and an algorithm that can check the canonicity of a given integral tetrahedron with at most 6 integer ...
arxiv  

Linear Multistep Numerical Methods for Ordinary Differential Equations [PDF]

arXiv, 2008
A review of the most popular Linear Multistep (LM) Methods for solving Ordinary Differential Equations numerically is presented. These methods are first derived from first principles, and are discussed in terms of their order, consistency, and various types of stability.
arxiv  

Hardy-Littlewood Constants Embedded into Infinite Products over All Positive Integers [PDF]

arXiv, 2009
A group of infinite products over low-order rational polynomials evaluated at the sequence of prime numbers is loosely called the Hardy-Littlewood constants. In this manuscript we look at them as factors embedded in a super-product over primes, semiprimes, 3-almost primes etc.
arxiv  

Geometrically convergent sequences of upper and lower bounds on the Wallis ratio and related expressions [PDF]

Math. Inequal. Appl., 18 (1):195--205, 2015, 2011
Sequences of algebraic upper and lower bounds on the Wallis ratio are given with the relative errors that converge to 0 geometrically and uniformly on any interval of the form [x_0,\infty) for x_0>-\frac12; moreover, the relative and absolute errors converge to 0 as x\to\infty.
arxiv  

Effect of relevant factors on radiation-induced nasopharyngeal ulcer in patients with primary nasopharyngeal carcinoma treated with intensity-modulated radiation therapy. [PDF]

Laryngoscope Investig Otolaryngol, 2020
Fei Z, Chen T, Qiu X, Chen C.
europepmc   +1 more source