RCSEDv2: analytic approximations of k-corrections for galaxies out to redshift $z=1$

To compare photometric properties of galaxies at different redshifts, we need to correct fluxes for the change of effective rest-frame wavelengths of filter bandpasses, called $k$-corrections. At redshifts $z>0.3$, the wavelength shift becomes so large that typical broadband photometric bands shift into the neighboring rest frame band. At $z=0.6-0.8$ the shift reaches two or even three bands. Therefore, we need perform $k$-corrections from one observed bandpass to another. Here we expand the methodology proposed by Chilingarian et al. (2010) and fit cross-band $k$-corrections by smooth low-order polynomial functions of one observed color and a redshift - this approach but without cross-band is implemented as standard functions in {\sc topcat}, which can be used for galaxies at $z<0.5$. We also computed analytic approximations for WISE bands, which were not available in the past. We now have a complete set of $k$-corrections coefficients, which allow us to process photometric measurements for galaxies out to redshift $z=1$. We calculated standard and cross-band $k$-corrections for about 4 million galaxies in second Reference Catalog of Spectral Energy Distributions (RCSEDv2) of galaxies and we showed that, in cases of widely used UV, optical and near-infrared filters, our analytic approximations work very well and can be used for extragalactic data from future wide-field surveys.