# §12.20 Approximations

Luke (1969b, pp. 25 and 35) gives Chebyshev-series expansions for the confluent hypergeometric functions and 13.2(i)) whose regions of validity include intervals with endpoints and , respectively. As special cases of these results a Chebyshev-series expansion for valid when follows from (12.7.14), and Chebyshev-series expansions for and valid when follow from (12.4.1), (12.4.2), (12.7.12), and (12.7.13). Here denotes an arbitrary positive constant.