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S ince Ihe sine, cosine, expone ntial int egral s a nd hype rbo li c s ine, a nd cos ine inl egra ls a re frequently enco unte red togethe r in phys ical proble ms and the ir ex pans ion s ha ve te rm s 111 co mmon , we have inco rpo rated these fun ction s into P a rt Ill. (For P a rt s I and II , see . I). While acc uracy ove r the e ntire domain of definition rema in s o ur main co ncern , we have te nded toward me thod s that also e nsure e ffi c ie ncy, portability, and ease of programming and modifi ca tion. The numbe r of te rm s in se ri es, the numbe r of conve rge nt s in an ite rative process, the s tarting argumen ts fo r d ifferent method s, are aU de termined by the program as a function of word le ngth, argume nts, accuracy des ired , e tc . More re ali sti c res ult s are re turned whe n erro r conditio ns a re encounte red. The proper analytic behavior of the fun c tion wiU always be re tained to furth e r e nsure correct limiting values, in particular of re lated fun ctions and fo r purposes of diffe re nti a tion a nd integration. In Pa11.s I and Il in add ition to the implementing ANS FORTRAN program , we had inc luded a driver (test) program and its results . S in ce e ithe r of these driver program s can be readi ly mod ifi ed to compute other fun ctions, we have omitted the drive r program and in place of it s resu lt s have included a table of co rrect results to 3.5 s ignificant figures cove rin g essentiall y the fun c tional ran ge of prese nt computers.

Automatic computing methods for special functions. Part III. The sine, cosine, exponential integrals, and related functions