Basic Methods for Computing Special Functions

This paper gives an overview of methods for the numerical evaluation of special functions, that is, the functions that arise in many problems from mathematical physics, engineering, probability theory, and other applied sciences. We consider in detail a selection of basic methods which are frequently used in the numerical evaluation of special functions: converging and asymptotic series, including Chebyshev expansions, linear recurrence relations, and numerical quadrature. Several other methods are available and some of these will be discussed in less detail. We give examples of recent software for special functions where these methods are used. We mention a list of new publications on computational aspects of special functions available on our website

Spectral characterisation of analog samples in anticipation of OSIRS-REx's arrival at Bennu: A blind test study

We present spectral measurements of a suite of mineral mixtures and meteorites that are possible analogs for asteroid (101955) Bennu, the target asteroid for NASA's Origins, Spectral Interpretation, Resource Identification, Security, Regolith Explorer (OSIRIS-REx) mission. The sample suite, which includes anhydrous and hydrated mineral mixtures and a suite of chondritic meteorites (CM, CI, CV, CR, and L5), was chosen to characterize the spectral effects due to varying amounts of aqueous alteration and minor amounts of organic material. Our results demonstrate the utility of mineral mixtures for understanding the mixing behavior of meteoritic materials and identifying spectrally dominant species across the visible to near-infrared (VNIR) and thermal infrared (TIR) spectral ranges. Our measurements demonstrate that, even with subtle signatures in the spectra of chondritic meteorites, we can identify diagnostic features related to the minerals comprising each of the samples. Also, the complementary nature of the two spectral ranges regarding their ability to detect different mixture and meteorite components can be used to characterize analog sample compositions better. However, we observe differences in the VNIR and TIR spectra between the mineral mixtures and the meteorites. These differences likely result from (1) differences in the types and physical disposition of constituents in the mixtures versus in meteorites, (2) missing phases observed in meteorites that we did not add to the mixtures, and (3) albedo differences among the samples. In addition to the initial characterization of the analog samples, we will use these spectral measurements to test phase detection and abundance determination algorithms in anticipation of mapping Bennu's surface properties and selecting a sampling site