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in terms of elementary functions

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1: 9.19 Approximations
§9.19(i) Approximations in Terms of Elementary Functions
2: 18.32 OP’s with Respect to Freud Weights
However, for asymptotic approximations in terms of elementary functions for the OP’s, and also for their largest zeros, see Levin and Lubinsky (2001) and Nevai (1986). …
3: 18.24 Hahn Class: Asymptotic Approximations
In particular, asymptotic formulas in terms of elementary functions are given when z = x is real and fixed. … Dunster (2001b) provides various asymptotic expansions for C n ( x ; a ) as n , in terms of elementary functions or in terms of Bessel functions. …
4: 7.24 Approximations
§7.24(i) Approximations in Terms of Elementary Functions
5: 6.20 Approximations
§6.20(i) Approximations in Terms of Elementary Functions
6: 12.10 Uniform Asymptotic Expansions for Large Parameter
With the upper sign in (12.10.2), expansions can be constructed for large μ in terms of elementary functions that are uniform for t ( - , ) 2.8(ii)). … The turning points can be included if expansions in terms of Airy functions are used instead of elementary functions2.8(iii)). …
§12.10(ii) Negative a , 2 - a < x <
12.10.30 v ¯ s ( t ) = i s v s ( - i t ) .
§12.10(vi) Modifications of Expansions in Elementary Functions
7: 25.5 Integral Representations
§25.5(i) In Terms of Elementary Functions
8: 33.20 Expansions for Small | ϵ |
These expansions are in terms of elementary functions, Airy functions, and Bessel functions of orders 2 + 1 and 2 + 2 .
9: 28.8 Asymptotic Expansions for Large q
With additional restrictions on z , uniform asymptotic approximations for solutions of (28.2.1) and (28.20.1) are also obtained in terms of elementary functions by re-expansions of the Whittaker functions; compare §2.8(ii). Subsequently the asymptotic solutions involving either elementary or Whittaker functions are identified in terms of the Floquet solutions me ν ( z , q ) 28.12(ii)) and modified Mathieu functions M ν ( j ) ( z , h ) 28.20(iii)). …
10: 12.14 The Function W ( a , x )
Positive a , 2 a < x <