Lax%20pairs
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11—20 of 170 matching pages
11: 8 Incomplete Gamma and Related
Functions
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12: 28 Mathieu Functions and Hill’s Equation
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13: Bibliography F
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Sur certaines sommes des intégral-cosinus.
Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
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Tables of Elliptic Integrals of the First, Second, and Third Kind.
Technical report
Technical Report ARL 64-232, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio.
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On weighted polynomial approximation on the whole real axis.
Acta Math. Acad. Sci. Hungar. 20, pp. 223–225.
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Characteristic values of the integral equation satisfied by the Mathieu functions and its application to a system with chirality-pair interaction on a one-dimensional lattice.
Phys. A 190 (3-4), pp. 346–362.
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14: 8.26 Tables
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Khamis (1965) tabulates for , to 10D.
Abramowitz and Stegun (1964, pp. 245–248) tabulates for , to 7D; also for , to 6S.
Pagurova (1961) tabulates for , to 4-9S; for , to 7D; for , to 7S or 7D.
Zhang and Jin (1996, Table 19.1) tabulates for , to 7D or 8S.
15: 23 Weierstrass Elliptic and Modular
Functions
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16: 24.19 Methods of Computation
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►For number-theoretic applications it is important to compute for ; in particular to find the irregular pairs
for which .
We list here three methods, arranged in increasing order of efficiency.
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17: 28.8 Asymptotic Expansions for Large
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28.8.1
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►Barrett (1981) supplies asymptotic approximations for numerically satisfactory pairs of solutions of both Mathieu’s equation (28.2.1) and the modified Mathieu equation (28.20.1).
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►Dunster (1994a) supplies uniform asymptotic approximations for numerically satisfactory pairs of solutions of Mathieu’s equation (28.2.1).
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18: 36 Integrals with Coalescing Saddles
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19: Gergő Nemes
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►As of September 20, 2021, Nemes performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 25 Zeta and Related Functions.
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20: Wolter Groenevelt
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►As of September 20, 2022, Groenevelt performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 18 Orthogonal Polynomials.
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