Watson expansions
(0.002 seconds)
1—10 of 40 matching pages
1: 20.8 Watson’s Expansions
§20.8 Watson’s Expansions
…2: 11.11 Asymptotic Expansions of Anger–Weber Functions
3: 2.4 Contour Integrals
…
βΊ
§2.4(i) Watson’s Lemma
…4: 2.3 Integrals of a Real Variable
…
βΊ
§2.3(ii) Watson’s Lemma
… βΊThe desired uniform expansion is then obtained formally as in Watson’s lemma and Laplace’s method. …5: 11.2 Definitions
…
βΊ
§11.2(i) Power-Series Expansions
… βΊThe expansions (11.2.1) and (11.2.2) are absolutely convergent for all finite values of . …6: 11.9 Lommel Functions
…
βΊand
…
βΊFor the foregoing results and further information see Watson (1944, §§10.7–10.73) and Babister (1967, §3.16).
βΊ
§11.9(ii) Expansions in Series of Bessel Functions
… βΊ§11.9(iii) Asymptotic Expansion
… βΊFor further information on Lommel functions see Watson (1944, §§10.7–10.75) and Babister (1967, Chapter 3). …7: 5.11 Asymptotic Expansions
…
βΊThe expansion (5.11.1) is called Stirling’s series (Whittaker and Watson (1927, §12.33)), whereas the expansion (5.11.3), or sometimes just its leading term, is known as Stirling’s formula (Abramowitz and Stegun (1964, §6.1), Olver (1997b, p. 88)).
…
8: 10.40 Asymptotic Expansions for Large Argument
§10.40 Asymptotic Expansions for Large Argument
βΊ§10.40(i) Hankel’s Expansions
… βΊProducts
… βΊ … βΊ§10.40(iv) Exponentially-Improved Expansions
…9: 11.10 Anger–Weber Functions
…
βΊ
§11.10(iii) Maclaurin Series
… βΊThese expansions converge absolutely for all finite values of . … βΊ
11.10.19
…
βΊwhere
…
βΊ