Redshift-Space Distortions of the Correlation Function in Wide-Angle Galaxy Surveys

Using a novel two-dimensional coordinate system, we have derived a particularly simple way to express the redshift distortions in galaxy redshift surveys with arbitrary geometry in closed form. This method provides an almost ideal way to measure the value of β=Ω^0.6₀/b in wide area surveys, since all pairs in the survey can be used for the analysis. In the limit of small angles, this result straightforwardly reduces to the plane-parallel approximation. This expansion can also be used together with more sophisticated methods such as the calculation of Karhunen-Loève eigenvectors in redshift space for an arbitrary survey geometry. Therefore, these results should provide more precise methods in which to measure the large-scale power spectrum and the value of β simultaneously.