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11—20 of 240 matching pages
11: Bibliography K
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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
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Methods of computing the Riemann zeta-function and some generalizations of it.
USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I.
Inverse Problems 20 (4), pp. 1165–1206.
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The Askey scheme as a four-manifold with corners.
Ramanujan J. 20 (3), pp. 409–439.
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Algorithm 421. Complex gamma function with error control.
Comm. ACM 15 (4), pp. 271–272.
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12: Possible Errors in DLMF
Possible Errors in DLMF
… ►One source of confusion, rather than actual errors, are some new functions which differ from those in Abramowitz and Stegun (1964) by scaling, shifts or constraints on the domain; see the Info box (click or hover over the icon) for links to defining formula. …Errors in the printed Handbook may already have been corrected in the online version; please consult Errata. ►Nevertheless, it is quite possible that errors remain and we would appreciate knowing about them, so that we can make the necessary corrections. …13: Bibliography N
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Error bounds for the asymptotic expansion of the Hurwitz zeta function.
Proc. A. 473 (2203), pp. 20170363, 16.
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Error bounds and exponential improvement for Hermite’s asymptotic expansion for the gamma function.
Appl. Anal. Discrete Math. 7 (1), pp. 161–179.
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Error bounds and exponential improvement for the asymptotic expansion of the Barnes -function.
Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 470 (2172), pp. 20140534, 14.
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Error bounds and exponential improvements for the asymptotic expansions of the gamma function and its reciprocal.
Proc. Roy. Soc. Edinburgh Sect. A 145 (3), pp. 571–596.
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A table of integrals of the error functions.
J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.
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14: 2.7 Differential Equations
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►For error bounds for (2.7.14) see Olver (1997b, Chapter 7).
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►For irregular singularities of nonclassifiable rank, a powerful tool for finding the asymptotic behavior of solutions, complete with error bounds, is as follows:
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2.7.23
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►Here is the error-control function
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2.7.24
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15: 7.1 Special Notation
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►Unless otherwise noted, primes indicate derivatives with respect to the argument.
►The main functions treated in this chapter are the error function ; the complementary error functions and ; Dawson’s integral ; the Fresnel integrals , , and ; the Goodwin–Staton integral ; the repeated integrals of the complementary error function ; the Voigt functions and .
►Alternative notations are , , , , , , , .
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16: 7.10 Derivatives
17: 7.17 Inverse Error Functions
§7.17 Inverse Error Functions
►§7.17(i) Notation
►The inverses of the functions , , , are denoted by … ►§7.17(ii) Power Series
… ►§7.17(iii) Asymptotic Expansion of for Small
…18: 7.3 Graphics
19: 15.19 Methods of Computation
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►The accuracy is controlled and validated by a running error analysis coupled with interval arithmetic.