High-redshift cosmography: Application and comparison with different methods

Cosmography is used in cosmological data processing order to constrain the kinematics of universe a model-independent way. In this paper, we first investigate effect ultraviolet (UV) and X-ray relation quasar on constraints. By fitting cosmographic parameters simultaneously, find that 4$\sigma$ deviation from constant cold dark matter ($\Lambda$CDM) model disappears. Next, utilizing Pantheon sample 31 long gamma-ray bursts (LGRBs), make comparison among different expansions ($z$-redshift, $y$-redshift, $E(y)$, $\log(1+z)$, $\log(1+z)+k_{ij}$, Pad$\rm \acute{e}$ approximations) with third-order fourth-order expansions. The expansion can significantly affect results, especially for $y$-redshift method. Through analysis same sample, lower-order preferable, except $E(y)$ methods. For methods, despite adopting parameterization $y=z/(1+z)$, performance latter better than former. Logarithmic polynomials, $\log(1+z)$ $\log(1+z) + k_{ij}$, perform $z$-redshift, but worse approximations. Finally, comprehensively analyze results obtained samples. We \acute{e}_{(2,1)}$ method suitable both low high redshift cases. \acute{e}_{(2,2)}$ performs well high-redshift situation. only constraint two ($q_{0}$ $j_{0}$) reliable.