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1: 30.9 Asymptotic Approximations and Expansions
§30.9(i) Prolate Spheroidal Wave Functions
… ►2: 12.10 Uniform Asymptotic Expansions for Large Parameter
§12.10 Uniform Asymptotic Expansions for Large Parameter
… ►§12.10(vi) Modifications of Expansions in Elementary Functions
… ► … ►Modified Expansions
… ►3: 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.
Zhang and Jin (1996, pp. 533–535) includes the zeros (in degrees) of , for , and the first 5 zeros of , for or , . Precision is mostly 9S.