Aitken%20%CE%942-process
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1: 3.9 Acceleration of Convergence
§3.9(iii) Aitken’s -Process
… ►When applied repeatedly, Aitken’s process is known as the iterated -process. … … ►Shanks’ transformation is a generalization of Aitken’s -process. … ►Aitken’s -process is the case . …2: 20 Theta Functions
Chapter 20 Theta Functions
…3: 28.1 Special Notation
4: 2.11 Remainder Terms; Stokes Phenomenon
5: 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.
6: 8 Incomplete Gamma and Related
Functions
7: 28 Mathieu Functions and Hill’s Equation
8: 8.26 Tables
Khamis (1965) tabulates for , to 10D.
Abramowitz and Stegun (1964, pp. 245–248) tabulates for , to 7D; also for , to 6S.
Pagurova (1961) tabulates for , to 4-9S; for , to 7D; for , to 7S or 7D.
Zhang and Jin (1996, Table 19.1) tabulates for , to 7D or 8S.