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449 one finds that for y = Fo (e) C= :n; V3 [Po (2'Yj) 3 -kjF(i) + (2'Yj)! Fd (2'Yj) 3 -ijF (·m, } 1 (14.17) C2 = :n; [- (2'Yj)! Fd (2'Yj) 3 -ijF(i) + Fo (2'Yj) 3 -~;r(i)J, and if y is to be Go(e), C and Chave the same form with Go (2'Yj) replacing Po (2'Yj) 1 2 and G~(2'Yj) replacing Fd(2'Yj). The values of the functions at eo =2'Yj may be ob tained from (14.8). 1 J.K. TYSON has employed the modified Hankel functions of order one third 2 as solutions of (13.4) to obtain expressions for the Coulomb functions for L =0 which converge near e =2'Yj. His results appear as linear combinations of the real and imaginary parts of n ~(x) = (12)!e- ;/6 [A;{- x) - iB;( -x)J, (14.18) and its derivatives multiplying power series in x = (e - 2'Yj)j(2'Yj)1. For values 1 away from the turning point for L =0, TYSON has obtained forms for Po{e) and Go(e) which are similar to (13.1) to (13.3). The JWKB approximation is again the leading term, and some higher order corrections are given. Expressions similar to Eqs. (14.11) and (14.12) have been obtained by T.D. 3 NEWTON employing the integral representation of (4.4). His results give re presentations of FL(e), Gde) in the vicinity of e=2'Yj [whereas (14.11), (14.12) converge near e=eLJ when L.
Sects. 12, 13. 89 sequence and that subgiant and fainter stars in globular clusters have ultraviolet excesses. When dealing with stars whose physical properties are imperfectly under stood, such as in globular cluster stars, we cannot rely too heavily on the empiri cal calibration by the kinds of stars used to define Fig. 5, to determine their true, unreddened U-B, B-V curve. But if by a combination of arguments, principally the reddening in the region of the stars we do known about, we can assign a fairly probable unreddened U-B, B-V curve to a group of stars about which we know little, the argument may be turned around. In this case some information may be gained about the energy envelope of the stars by examining the differences between the normal two-color index curves for the unknown group of stars compared to the known. In general there seem to be two possible causes for different stars defining different normal sequences in the U-B, B-V plane. One, the relative energy distribution in the continuum in the U, B and V photometry bands are different. An example of this is the effect of the Balmer depression in supergiants. This, of course, requires deviation from black body radiation curves for one or both groups of stars. This cause seems to be the dominant effect for very blue, hot stars where the depression of the continuum by absorption lines is at a minimum.