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21: Bibliography O
22: Bibliography N
23: 3.8 Nonlinear Equations
24: 28.18 Integrals and Integral Equations
§28.18 Integrals and Integral Equations
…25: 28.35 Tables
§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.
26: 28.1 Special Notation
integers. | |
… | |
real or complex parameters of Mathieu’s equation with . | |
… |
, | , | , | , | , |
Abramowitz and Stegun (1964, Chapter 20)
…27: 32.8 Rational Solutions
§32.8(ii) Second Painlevé Equation
… ►§32.8(iii) Third Painlevé Equation
… ►§32.8(iv) Fourth Painlevé Equation
… ►§32.8(v) Fifth Painlevé Equation
… ►28: Bibliography F
29: 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.
Zhang and Jin (1996, p. 337) tabulates , , , for to 8S and for to 9D.
Sherry (1959) tabulates , , , , ; 20S.
Zhang and Jin (1996, p. 339) tabulates , , , , , , , , ; 8D.