The Converging Factors for the Sine and Cosine Integrals
DAVID W TAYLOR NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER BETHESDA MD COMPUTATION MATHEMATICS/LOGISTICS DEPT
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The theory of the converging factors for the sine and cosine integrals is developed and then applied to the calculation on a CDC 6700 system of tables of these factors and their reduced derivatives to about 35 decimal places. The factors are then used in conjunction with appropriately truncated asymptotic series to produce tables of six, Six, and Cix to 28 decimals by a computer program, for successive integer values of x ranging from 1 to 70, inclusive. Interpolation in the tables by Taylor series is illustrated by numerical examples, which include a new, extended calculation of the Gibbs constant.
- Numerical Mathematics