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11—20 of 40 matching pages
11: 22.21 Tables
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►Spenceley and Spenceley (1947) tabulates , , , , for and to 12D, or 12 decimals of a radian in the case of .
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12: 25.19 Tables
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13: 28.35 Tables
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Ince (1932) includes eigenvalues , , and Fourier coefficients for or , ; 7D. Also , for , , corresponding to the eigenvalues in the tables; 5D. Notation: , .
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.
Blanch and Clemm (1969) includes eigenvalues , for , , , ; 4D. Also and for , , and , respectively; 8D. Double points for ; 8D. Graphs are included.
14: About Color Map
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►In particular, the colors at 90 and 180 degrees are some vague greenish and purplish hues.
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15: Bibliography E
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Algorithm 934: Fortran 90 subroutines to compute Mathieu functions for complex values of the parameter.
ACM Trans. Math. Softw. 40 (1), pp. 8:1–8:19.
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Algorithm 861: Fortran 90 subroutines for computing the expansion coefficients of Mathieu functions using Blanch’s algorithm.
ACM Trans. Math. Software 32 (4), pp. 622–634.
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16: 29.7 Asymptotic Expansions
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29.7.7
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17: 35.2 Laplace Transform
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18: Bibliography N
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Der Eulersche Dilogarithmus und seine Verallgemeinerungen.
Nova Acta Leopoldina 90, pp. 123–212.
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19: 4.10 Integrals
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►Extensive compendia of indefinite and definite integrals of logarithms and exponentials include Apelblat (1983, pp. 16–47), Bierens de Haan (1939), Gröbner and Hofreiter (1949, pp. 107–116), Gröbner and Hofreiter (1950, pp. 52–90), Gradshteyn and Ryzhik (2000, Chapters 2–4), and Prudnikov et al. (1986a, §§1.3, 1.6, 2.3, 2.6).
20: 20.4 Values at = 0
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