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

J/ψ Production At Low Pt In Au+au And Cu+cu Collisions At Snn =200 Gev With The Star Detector

The J/ψ pT spectrum and nuclear modification factor (RAA) are reported for pT<5GeV/c and |y|<1 from 0% to 60% central Au+Au and Cu+Cu collisions at sNN=200GeV at STAR. A significant suppression of pT-integrated J/ψ production is observed in central Au+Au events. The Cu+Cu data are consistent with no suppression, although the precision is limited by the available statistics. RAA in Au+Au collisions exhibits a strong suppression at low transverse momentum and gradually increases with pT. The data are compared to high-pT STAR results and previously published BNL Relativistic Heavy Ion Collider results. Comparing with model calculations, it is found that the invariant yields at low pT are significantly above hydrodynamic flow predictions but are consistent with models that include color screening and regeneration. © 2014 American Physical Society.902CNRS/IN2P3; NSF; Arthritis National Research Foundation; NRF-2012004024; ANRF; Arthritis National Research FoundationMatsui, T., Satz, H., (1986) Phys Lett. B, 178, p. 416. , PYLBAJ 0370-2693 10.1016/0370-2693(86)91404-8Digal, S., Petreczky, P., Satz, H., (2001) Phys. Rev. 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Measurement Of Charge Multiplicity Asymmetry Correlations In High-energy Nucleus-nucleus Collisions At Snn =200 Gev

A study is reported of the same- and opposite-sign charge-dependent azimuthal correlations with respect to the event plane in Au+Au collisions at sNN=200 GeV. The charge multiplicity asymmetries between the up/down and left/right hemispheres relative to the event plane are utilized. The contributions from statistical fluctuations and detector effects were subtracted from the (co-)variance of the observed charge multiplicity asymmetries. In the mid- to most-central collisions, the same- (opposite-) sign pairs are preferentially emitted in back-to-back (aligned on the same-side) directions. The charge separation across the event plane, measured by the difference, Δ, between the like- and unlike-sign up/down-left/right correlations, is largest near the event plane. 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