asymptotic%20approximations%20of%20sums%20and%20sequences
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11: 27.2 Functions
12: 30.9 Asymptotic Approximations and Expansions
13: Bibliography F
14: 6.20 Approximations
Cody and Thacher (1968) provides minimax rational approximations for , with accuracies up to 20S.
Cody and Thacher (1969) provides minimax rational approximations for , with accuracies up to 20S.
MacLeod (1996b) provides rational approximations for the sine and cosine integrals and for the auxiliary functions and , with accuracies up to 20S.
15: 10.75 Tables
Achenbach (1986) tabulates , , , , , 20D or 18–20S.
Bickley et al. (1952) tabulates or , or , , (.01 or .1) 10(.1) 20, 8S; , , , or , 10S.
Kerimov and Skorokhodov (1984b) tabulates all zeros of the principal values of and , for , 9S.
Olver (1960) tabulates , , , , , , 8D. Also included are tables of the coefficients in the uniform asymptotic expansions of these zeros and associated values as .
Zhang and Jin (1996, p. 322) tabulates , , , , , , , , , 7S.
16: Bibliography D
17: Bibliography L
18: Bibliography R
19: 25.20 Approximations
Cody et al. (1971) gives rational approximations for in the form of quotients of polynomials or quotients of Chebyshev series. The ranges covered are , , , . Precision is varied, with a maximum of 20S.