psi%20function
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1: 9.18 Tables
Miller (1946) tabulates , for , for ; , for ; , for ; , , , (respectively , , , ) for . Precision is generally 8D; slightly less for some of the auxiliary functions. Extracts from these tables are included in Abramowitz and Stegun (1964, Chapter 10), together with some auxiliary functions for large arguments.
2: 36.2 Catastrophes and Canonical Integrals
3: 5.22 Tables
§5.22(ii) Real Variables
►Abramowitz and Stegun (1964, Chapter 6) tabulates , , , and for to 10D; and for to 10D; , , , , , , , and for to 8–11S; for to 20S. Zhang and Jin (1996, pp. 67–69 and 72) tabulates , , , , , , , and for to 8D or 8S; for to 51S. ►§5.22(iii) Complex Variables
… ►This reference also includes for the same arguments to 5D. …4: Bibliography D
5: 10.73 Physical Applications
§10.73(iii) Kelvin Functions
… ►§10.73(iv) Bickley Functions
…6: 19.36 Methods of Computation
§19.36(iii) Via Theta Functions
… ►For computation of Legendre’s integral of the third kind, see Abramowitz and Stegun (1964, §§17.7 and 17.8, Examples 15, 17, 19, and 20). … ►When the values of complete integrals are known, addition theorems with (§19.11(ii)) ease the computation of functions such as when is small and positive. …7: Errata
A sentence and unnumbered equation
were added which indicate that care must be taken with the multivalued functions in (19.11.5). See (Cayley, 1961, pp. 103-106).
Suggested by Albert Groenenboom.
Scales were corrected in all figures. The interval was replaced by and replaced by . All plots and interactive visualizations were regenerated to improve image quality.
(a) Density plot. | (b) 3D plot. |
Figure 36.3.9: Modulus of hyperbolic umbilic canonical integral function .
(a) Density plot. | (b) 3D plot. |
Figure 36.3.10: Modulus of hyperbolic umbilic canonical integral function .
(a) Density plot. | (b) 3D plot. |
Figure 36.3.11: Modulus of hyperbolic umbilic canonical integral function .
(a) Density plot. | (b) 3D plot. |
Figure 36.3.12: Modulus of hyperbolic umbilic canonical integral function .
Reported 2016-09-12 by Dan Piponi.
Originally the first term on the right side of the equation for was . The correct factor is .
Reported 2013-07-25 by Christopher Künstler.