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1: 28.16 Asymptotic Expansions for Large
2: 28.35 Tables
Ince (1932) includes eigenvalues , , and Fourier coefficients for or , ; 7D. Also , for , , corresponding to the eigenvalues in the tables; 5D. Notation: , .
Kirkpatrick (1960) contains tables of the modified functions , for , , ; 4D or 5D.
National Bureau of Standards (1967) includes the eigenvalues , for with , and with ; Fourier coefficients for and for , , respectively, and various values of in the interval ; joining factors , for with (but in a different notation). Also, eigenvalues for large values of . Precision is generally 8D.
Zhang and Jin (1996, pp. 521–532) includes the eigenvalues , for , ; (’s) or 19 (’s), . Fourier coefficients for , , . Mathieu functions , , and their first -derivatives for , . Modified Mathieu functions , , and their first -derivatives for , , . Precision is mostly 9S.
3: 27.15 Chinese Remainder Theorem
4: Bibliography N
5: 12.11 Zeros
§12.11(ii) Asymptotic Expansions of Large Zeros
… ►When the zeros are asymptotically given by and , where is a large positive integer and … ►§12.11(iii) Asymptotic Expansions for Large Parameter
►For large negative values of the real zeros of , , , and can be approximated by reversion of the Airy-type asymptotic expansions of §§12.10(vii) and 12.10(viii). … ►6: 28.8 Asymptotic Expansions for Large
§28.8 Asymptotic Expansions for Large
… ►§28.8(ii) Sips’ Expansions
… ►§28.8(iii) Goldstein’s Expansions
… ►Barrett’s Expansions
… ►7: Bibliography O
8: 16.22 Asymptotic Expansions
9: 30.9 Asymptotic Approximations and Expansions
§30.9(i) Prolate Spheroidal Wave Functions
… ►10: Staff
Ronald F. Boisvert, Editor at Large, NIST
William P. Reinhardt, University of Washington, Chaps. 20, 22, 23
Peter L. Walker, American University of Sharjah, Chaps. 20, 22, 23
William P. Reinhardt, University of Washington, for Chaps. 20, 22, 23
Peter L. Walker, American University of Sharjah, for Chaps. 20, 22, 23