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11: 20 Theta Functions
Chapter 20 Theta Functions
…12: 28.16 Asymptotic Expansions for Large
13: 10.73 Physical Applications
§10.73(ii) Spherical Bessel Functions
…14: Bibliography O
15: Bibliography N
16: 3.8 Nonlinear Equations
17: 28.18 Integrals and Integral Equations
§28.18 Integrals and Integral Equations
…18: 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.
19: 28.1 Special Notation
integers. | |
… | |
real or complex parameters of Mathieu’s equation with . | |
… |
, | , | , | , | , |