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21: 3.11 Approximation Techniques
22: 8.26 Tables
Pearson (1965) tabulates the function () for , to 7D, where rounds off to 1 to 7D; also for , to 5D.
Pearson (1968) tabulates for , , with , to 7D.
Pagurova (1961) tabulates for , to 4-9S; for , to 7D; for , to 7S or 7D.
Stankiewicz (1968) tabulates for , to 7D.
Zhang and Jin (1996, Table 19.1) tabulates for , to 7D or 8S.
23: 21.1 Special Notation
positive integers. | |
… | |
th element of vector . | |
… | |
Transpose of . | |
… | |
. | |
… | |
set of all elements of the form “”. | |
set of all elements of , modulo elements of . Thus two elements of are equivalent if they are both in and their difference is in . (For an example see §20.12(ii).) | |
… |
24: 19.29 Reduction of General Elliptic Integrals
25: Bibliography K
26: 4.17 Special Values and Limits
27: Bibliography E
28: 9.18 Tables
Harvard University (1945) tabulates the real and imaginary parts of , , , for , , , with interval 0.1 in and . Precision is 8D. Here , .
Sherry (1959) tabulates , , , , ; 20S.
Zhang and Jin (1996, p. 339) tabulates , , , , , , , , ; 8D.
National Bureau of Standards (1958) tabulates and for and ; for . Precision is 8D.
29: 24.19 Methods of Computation
§24.19(ii) Values of Modulo
…30: 6.19 Tables
Abramowitz and Stegun (1964, Chapter 5) includes , , , , ; , , , , ; , , , , ; , , , , ; , , . Accuracy varies but is within the range 8S–11S.
Zhang and Jin (1996, pp. 652, 689) includes , , , 8D; , , , 8S.
Abramowitz and Stegun (1964, Chapter 5) includes the real and imaginary parts of , , , 6D; , , , 6D; , , , 6D.
Zhang and Jin (1996, pp. 690–692) includes the real and imaginary parts of , , , 8S.