Sines
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11—20 of 300 matching pages
11: 4.32 Inequalities
12: 4.47 Approximations
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►Clenshaw (1962) and Luke (1975, Chapter 3) give 20D coefficients for , , , , , , , , .
Schonfelder (1980) gives 40D coefficients for , , .
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►Hart et al. (1968) give , , , , , , , , , , , , , .
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►Luke (1975, Chapter 3) supplies real and complex approximations for , , , , , , .
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13: 6 Exponential, Logarithmic, Sine, and
Cosine Integrals
Chapter 6 Exponential, Logarithmic, Sine, and Cosine Integrals
…14: 4.18 Inequalities
15: 4.28 Definitions and Periodicity
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4.28.1
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4.28.3
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4.28.8
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►The functions and have period , and has period .
The zeros of and are and , respectively, .
16: 6.14 Integrals
17: 6.20 Approximations
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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).
Luke (1969b, pp. 41–42) gives Chebyshev expansions of , , and for , . The coefficients are given in terms of series of Bessel functions.
Luke (1969b, p. 25) gives a Chebyshev expansion near infinity for the confluent hypergeometric -function (§13.2(i)) from which Chebyshev expansions near infinity for , , and follow by using (6.11.2) and (6.11.3). Luke also includes a recursion scheme for computing the coefficients in the expansions of the functions. If the scheme can be used in backward direction.