Filon%20rule
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11—20 of 126 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: 8.25 Methods of Computation
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►See Allasia and Besenghi (1987b) for the numerical computation of from (8.6.4) by means of the trapezoidal rule.
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►A numerical inversion procedure is also given for calculating the value of (with 10S accuracy), when and are specified, based on Newton’s rule (§3.8(ii)).
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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: 9.17 Methods of Computation
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►The trapezoidal rule (§3.5(i)) is then applied.
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►Zeros of the Airy functions, and their derivatives, can be computed to high precision via Newton’s rule (§3.8(ii)) or Halley’s rule (§3.8(v)), using values supplied by the asymptotic expansions of §9.9(iv) as initial approximations.
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17: Software Index
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►Please see our Software Indexing Policy for rules that govern the indexing of software in the DLMF.
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20 Theta Functions | |||||||||||||||||||||||||
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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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