1—10 of 271 matching pages
1: 17.16 Mathematical Applications
§17.16 Mathematical Applications►Many special cases of -series arise in the theory of partitions, a topic treated in §§27.14(i) and 26.9. In Lie algebras Lepowsky and Milne (1978) and Lepowsky and Wilson (1982) laid foundations for extensive interaction with -series. …
2: 4.47 Approximations
§4.47(i) Chebyshev-Series Expansions…
3: 12.20 Approximations
§12.20 Approximations►Luke (1969b, pp. 25 and 35) gives Chebyshev-series expansions for the confluent hypergeometric functions and (§13.2(i)) whose regions of validity include intervals with endpoints and , respectively. As special cases of these results a Chebyshev-series expansion for valid when follows from (12.7.14), and Chebyshev-series expansions for and valid when follow from (12.4.1), (12.4.2), (12.7.12), and (12.7.13). …
4: 16.20 Integrals and Series
§16.20 Integrals and Series… ►Series of the Meijer -function are given in Erdélyi et al. (1953a, §5.5.1), Luke (1975, §5.8), and Prudnikov et al. (1990, §6.11). …
5: 18.40 Methods of Computation
6: 4.33 Maclaurin Series and Laurent Series
§4.33 Maclaurin Series and Laurent Series…
7: 12.18 Methods of Computation
8: 6.20 Approximations
§6.20(ii) Expansions in Chebyshev Series… ►
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, pp. 321–322) covers and for (the Chebyshev coefficients are given to 20D); for (20D), and for (15D). Coefficients for the sine and cosine integrals are given on pp. 325–327.
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.