Related papers: Pulsar timing array analysis in a Legendre polynom…

Pulsar timing offers an independent avenue to test general relativity and alternative gravity theories. This requires an understanding of how metric polarizations beyond the familiar transverse tensor ones imprint as a stochastic…

A new kind of deformed calculus was introduced recently in studying of parabosonic coordinate representation. Based on this deformed calculus, a new deformation of Legendre polynomials is proposed in this paper, some properties and…

In this work, we present a generalized methodology for analyzing the convergence of quasi-optimal Taylor and Legendre approximations, applicable to a wide class of parameterized elliptic PDEs with finite-dimensional deterministic and…

We derive some identities and relations and extremal problems and minimization and Fourier development involving of integral Legendre polynomials.

A new Bayesian software package for the analysis of pulsar timing data is presented in the form of TempoNest which allows for the robust determination of the non-linear pulsar timing solution simultaneously with a range of additional…

Observations of pulsar timing provide strong constraints on scalar-tensor theories of gravity, but these constraints are traditionally quoted as limits on the microscopic parameters (like the Brans-Dicke coupling, for example) that govern…

Pulsar timing-array correlation measurements offer an exciting opportunity to test the nature of gravity in the cosmologically novel nanohertz gravitational wave regime. The stochastic gravitational wave background is assumed Gaussian and…

A simple regularization procedure is proposed for the Legendre function series of improved nearside-farside subamplitudes for charged particles elastic scattering. The procedure is the extension of the usual one which defines the partial…

The recent revelation that there are correlated period derivative and pulse shape changes in pulsars has dramatically changed our understanding of timing noise as well as the relationship between the radio emission and the properties of the…

Using Fourier and wavelet analysis, we critically re-assess the significance of our detection of periodic pulsations in coronal loops. We show that the proper identification of the frequency dependence and statistical properties of the…

Observations have revealed that nearly all galaxies contain supermassive black holes (SMBHs) at their centers. When galaxies merge, these SMBHs form SMBH binaries (SMBHBs) that emit low-frequency gravitational waves (GWs). The incoherent…

Over the past decade and a half, adoption of Bayesian inference in pulsar timing analysis has led to increasingly sophisticated models. The recent announcement of evidence for a stochastic background of gravitational waves by various pulsar…

Taking the examples of Legendre and Hermite orthogonal polynomials, we show how to interpret the fact that these orthogonal polynomials are moments of other orthogonal polynomials in terms of their associated Riordan arrays. We use these…

Searching for gravitational waves in pulsar timing array data is computationally intensive. The data is unevenly sampled, and the noise is heteroscedastic, necessitating the use of a time-domain likelihood function with attendant expensive…

Pulsar timing array experiments search for phenomena that produce angular correlations in the arrival times of signals from millisecond pulsars. The primary goal is to detect an isotropic and stochastic gravitational wave background. We use…

Timing noise in pulsars is often modelled with a Fourier-basis Gaussian process that follows a power law with periodic boundary conditions on the observation time, $T_\mathrm{span}$. However the actual noise processes can extend well below…

Radio timing observations of a millisecond pulsar in orbit around the Galactic centre black hole (BH) or a BH at the centre of globular clusters could answer foundational questions in astrophysics and fundamental physics. Pulsar radio…

Pulsar Timing Arrays (PTAs) have recently found strong evidence for low-frequency gravitational waves (GWs) in the nanohertz frequency regime. As GWs pass, they produce deviations in measured lengths and light-travel times. PTA experiments…

Accurately estimating the parameters of the nanohertz gravitational-wave background is essential for understanding its origin. The background is typically modeled with a power-law spectrum, parametrized with an amplitude $A$, which…

Pulsar's position, proper motion and parallax are important parameters in timing equations. It is a really challenging work to fit astrometric parameters accurately through pulsar timing, especially for pulsars that show irregular timing…