Derivatives with respect to the order of the Bessel function of the first kind [PDF]
arXiv, 2014 An explicit expression of the k-th derivative of the Bessel function $J_\nu(z)$, with respect to its order $\nu$, is given. Particularizations for the cases of positive or negative $\nu$ are considered.
arxiv
Numerical solutions of integrodifferential systems by hybrid of general block-pulse functions and the second Chebyshev polynomials [PDF]
arXiv, 2008 By applying hybrid functions of general block-pulse functions and the second Chebyshev polynomials,integrodifferential systems are converted into a system of algebraic equations. The approximate solutions of integrodifferential systems are derived. The numerical examples illustrate that the algorithms are valid.
arxiv
More accurate approximations for the Gamma function [PDF]
Thai J. Math., Volume 9, Issue 1, 2011, 21-28, 2010 A series transformation idea inspired by a formula of R. W. Gosper and some asymptotic expansions for the central binomial coefficients leads us to new accurate approximations for the Gamma function.
arxiv
Numerical Algorithms for the Computation of Generalized Prolate Spheroidal Functions [PDF]
arXiv, 2017 Generalized Prolate Spheroidal Functions (GPSF) are the eigenfunctions of the truncated Fourier transform, restricted to D-dimensional balls in the spatial domain and frequency domain. Despite their useful properties in many applications, GPSFs are often replaced by crude approximations.
arxiv
Some relations between the Riemann zeta function and the generalized Bernoulli polynomials of level $m$ [PDF]
arXiv, 2019 The main purpose of this paper is to show some relations between the Riemann zeta function and the generalized Bernoulli polynomials of level $m$. Our approach is based on the use of Fourier expansions for the periodic generalized Bernoulli functions of level $m$, as well as quadrature formulae of Euler-Maclaurin type.
arxiv
Truncation Error Analysis of Approximate Operators for a Moving Particle Semi-Implicit Method
, 2019 This paper considers several approximate operators used in a particle method based on a Voronoi diagram. Under some assumptions on a weight function, we derive truncation error estimates for our approximate gradient and Laplace operators.
Koba, Hajime, Sato, Kazuki
core
A mathematical model for simulating the spread of a disease through a country divided into geographical regions with different population densities. [PDF]
J Math Biol, 2022 Harris PJ, Bodmann BEJ.
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Behaviour of $L_{q}$ norms of the $\sinc_{p}$ function [PDF]
arXiv, 2018 An integral inequality due to Ball involves the $L_{q}$ norm of the $\sinc_p$ function; the dependence of this norm on $q$ as $q\rightarrow\infty$ is now understood. By use of recent inequalities involving $p-$trigonometric functions $(1
arxiv
Partial Differential Equations in Applied MathematicsThis study examines how Stratonovich integrals (SIs) affect the solutions of the Heisenberg ferromagnetic spin chain (HFSC) equation using the modified (G'/G)-expansion (MG'/GE) scheme.
Md. Nur Alam
doaj
Parabolic Cylinder Functions: Examples of Error Bounds For Asymptotic Expansions [PDF]
arXiv, 2002 Several asymptotic expansions of parabolic cylinder functions are discussed and error bounds for remainders in the expansions are presented. In particular Poincar{\'e}-type expansions for large values of the argument $z$ and uniform expansions for large values of the parameter are considered.
arxiv