Dougall%20expansion
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21—30 of 343 matching pages
21: Bibliography O
22: 9.7 Asymptotic Expansions
§9.7 Asymptotic Expansions
… ►Numerical values of are given in Table 9.7.1 for to 2D. … ►§9.7(ii) Poincaré-Type Expansions
… ►§9.7(v) Exponentially-Improved Expansions
… ►23: 30.9 Asymptotic Approximations and Expansions
§30.9 Asymptotic Approximations and Expansions
… ►§30.9(iii) Other Approximations and Expansions
…24: 25.12 Polylogarithms
25: 15.4 Special Cases
Dougall’s Bilateral Sum
…26: Bibliography W
27: 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.
Ince (1932) includes the first zero for , for or , ; 4D. This reference also gives zeros of the first derivatives, together with expansions for small .