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1: 8.21 Generalized Sine and Cosine Integrals
§8.21 Generalized Sine and Cosine Integrals
… ►§8.21(iv) Interrelations
… ►§8.21(v) Special Values
… ►§8.21(viii) Asymptotic Expansions
… ►2: 6.2 Definitions and Interrelations
§6.2(ii) Sine and Cosine Integrals
… ►Values at Infinity
… ►Hyperbolic Analogs of the Sine and Cosine Integrals
… ►§6.2(iii) Auxiliary Functions
►3: 20 Theta Functions
Chapter 20 Theta Functions
…4: Peter L. Walker
5: 6.19 Tables
§6.19(ii) Real Variables
►Abramowitz and Stegun (1964, Chapter 5) includes , , , , ; , , , , ; , , , , ; , , , , ; , , . Accuracy varies but is within the range 8S–11S.
Zhang and Jin (1996, pp. 652, 689) includes , , , 8D; , , , 8S.
Abramowitz and Stegun (1964, Chapter 5) includes the real and imaginary parts of , , , 6D; , , , 6D; , , , 6D.
Zhang and Jin (1996, pp. 690–692) includes the real and imaginary parts of , , , 8S.
6: 6.16 Mathematical Applications
7: 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.
Luke and Wimp (1963) covers for (20D), and and for (20D).