Empirical calibration of the near-infrared Ca ii triplet – III. Fitting functions

Using a near-infrared stellar library of 706 stars with a wide coverage of atmospheric parameters, we study the behaviour of the Ca  ii triplet strength in terms of effective temperature, surface gravity and metallicity. Empirical fitting functions for recently defined line-strength indices, namely CaT*, CaT and PaT, are provided. These functions can be easily implemented into stellar population models to provide accurate predictions for integrated Ca  ii strengths. We also present a thorough study of the various error sources and their relation to the residuals of the derived fitting functions. Finally, the derived functional forms and the behaviour of the predicted Ca  ii are compared with those of previous works in the field.