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incomplete Riemann zeta function

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11: Bibliography P
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  • V. I. Pagurova (1965) An asymptotic formula for the incomplete gamma function. Ε½. Vyčisl. Mat. i Mat. Fiz. 5, pp. 118–121 (Russian).
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    Notes:
    English translation in U.S.S.R. Computational Math. and Math. Phys. 5(1), pp. 162–166
    External Links:
    Document, MathReview (E. Lukacs), ZentralBlatt
    Referenced by:
    §8.11(iv).
    Encodings:
    BibTeX
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  • R. B. Paris (2002a) Error bounds for the uniform asymptotic expansion of the incomplete gamma function. J. Comput. Appl. Math. 147 (1), pp. 215–231.
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    External Links:
    ISSN 0377-0427, Document, MathReview, ZentralBlatt
    Referenced by:
    §8.12.
    Encodings:
    BibTeX
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  • R. B. Paris (2002b) A uniform asymptotic expansion for the incomplete gamma function. J. Comput. Appl. Math. 148 (2), pp. 323–339.
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  • K. Pearson (Ed.) (1968) Tables of the Incomplete Beta-function. 2nd edition, Published for the Biometrika Trustees at the Cambridge University Press, Cambridge.
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    External Links:
    MathReview, ZentralBlatt
    Referenced by:
    1st item.
    Encodings:
    BibTeX
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  • R. Piessens and M. Branders (1972) Chebyshev polynomial expansions of the Riemann zeta function. Math. Comp. 26 (120), pp. G1–G5.
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    External Links:
    ISSN 0025-5718, FullText, MathReview
    Referenced by:
    2nd item, 3rd item.
    Encodings:
    BibTeX
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    12: Bibliography T
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  • N. M. Temme (1979b) The asymptotic expansion of the incomplete gamma functions. SIAM J. Math. Anal. 10 (4), pp. 757–766.
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    External Links:
    ISSN 0036-1410, Document, MathReview (E. Riekstiņő), ZentralBlatt
    Referenced by:
    §8.12.
    Encodings:
    BibTeX
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  • N. M. Temme (1987) On the computation of the incomplete gamma functions for large values of the parameters. In Algorithms for approximation (Shrivenham, 1985), Inst. Math. Appl. Conf. Ser. New Ser., Vol. 10, pp. 479–489.
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    External Links:
    FullText, MathReview (G. Meinardus), ZentralBlatt
    Referenced by:
    §8.25(iii).
    Encodings:
    BibTeX
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  • N. M. Temme (1992a) Asymptotic inversion of incomplete gamma functions. Math. Comp. 58 (198), pp. 755–764.
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    External Links:
    ISSN 0025-5718, FullText, Document, MathReview (F. W. J. Olver), ZentralBlatt
    Referenced by:
    §8.12, §8.12.
    Encodings:
    BibTeX
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  • N. M. Temme (1995a) Asymptotics of zeros of incomplete gamma functions. Ann. Numer. Math. 2 (1-4), pp. 415–423.
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    Notes:
    Special functions (Torino, 1993)
    External Links:
    ISSN 1021-2655, FullText, MathReview (E. R. Love), ZentralBlatt
    Referenced by:
    §8.13(ii).
    Encodings:
    BibTeX
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  • E. C. Titchmarsh (1986b) The Theory of the Riemann Zeta-Function. 2nd edition, The Clarendon Press Oxford University Press, New York-Oxford.
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    Notes:
    Edited and with a preface by D. R. Heath-Brown
    External Links:
    ISBN 0-19-853369-1, MathReview (Matti Jutila), ZentralBlatt
    Referenced by:
    §20.10(i), §20.9(iii), (25.10.1), (25.10.2), (25.10.3), (25.10.4), §25.10(i), §25.10(ii), §25.10, (25.2.12), §25.2(iv), (25.5.13), (25.5.14), (25.5.5), §25.5(ii), (25.9.1), (25.9.2), (25.9.3), §25.9, Ch.25, §27.4.
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    13: Software Index
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    Open Source With Book Commercial
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    8 Incomplete Gamma and Related Functions
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    β–Ί‘βœ“’ indicates that a software package implements the functions in a section; ‘a’ indicates available functionality through optional or add-on packages; an empty space indicates no known support. … β–ΊIn the list below we identify four main sources of software for computing special functions. … β–Ί
  • Commercial Software.

    Such software ranges from a collection of reusable software parts (e.g., a library) to fully functional interactive computing environments with an associated computing language. Such software is usually professionally developed, tested, and maintained to high standards. It is available for purchase, often with accompanying updates and consulting support.

    • … β–ΊThe following are web-based software repositories with significant holdings in the area of special functions. …
    14: Bibliography C
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  • M. A. Chaudhry and S. M. Zubair (1994) Generalized incomplete gamma functions with applications. J. Comput. Appl. Math. 55 (1), pp. 99–124.
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    External Links:
    ISSN 0377-0427, Document, MathReview, ZentralBlatt
    Referenced by:
    §8.16.
    Encodings:
    BibTeX
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  • B. K. Choudhury (1995) The Riemann zeta-function and its derivatives. Proc. Roy. Soc. London Ser. A 450, pp. 477–499.
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    External Links:
    ISSN 0962-8444, FullText, MathReview, ZentralBlatt
    Referenced by:
    §25.18(i).
    Encodings:
    BibTeX
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  • R. Cicchetti and A. Faraone (2004) Incomplete Hankel and modified Bessel functions: A class of special functions for electromagnetics. IEEE Trans. Antennas and Propagation 52 (12), pp. 3373–3389.
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    External Links:
    ISSN 0018-926X, Document, MathReview (T. Erber), ZentralBlatt
    Referenced by:
    §10.46.
    Encodings:
    BibTeX
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  • W. J. Cody, K. E. Hillstrom, and H. C. Thacher (1971) Chebyshev approximations for the Riemann zeta function. Math. Comp. 25 (115), pp. 537–547.
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    External Links:
    ISSN 0025-5718, FullText, MathReview, ZentralBlatt
    Referenced by:
    1st item.
    Encodings:
    BibTeX
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  • A. Cruz, J. Esparza, and J. Sesma (1991) Zeros of the Hankel function of real order out of the principal Riemann sheet. J. Comput. Appl. Math. 37 (1-3), pp. 89–99.
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    External Links:
    ISSN 0377-0427, Document, MathReview (Boro Döring), ZentralBlatt
    Referenced by:
    §10.21(ix).
    Encodings:
    BibTeX
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    15: Bibliography S
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  • P. Sarnak (1999) Quantum Chaos, Symmetry and Zeta Functions. Lecture I, Quantum Chaos. In Current Developments in Mathematics, 1997 (Cambridge, MA), R. Bott (Ed.), pp. 127–144.
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    External Links:
    MathReview (Shin-ya Koyama), ZentralBlatt
    Referenced by:
    §25.17.
    Encodings:
    BibTeX
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  • R. Sitaramachandrarao and B. Davis (1986) Some identities involving the Riemann zeta function. II. Indian J. Pure Appl. Math. 17 (10), pp. 1175–1186.
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    External Links:
    ISSN 0019-5588, MathReview (Jean-Marie De Koninck), ZentralBlatt
    Referenced by:
    §24.14(ii).
    Encodings:
    BibTeX
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  • P. Spellucci and P. Pulay (1975) Effective calculation of the incomplete gamma function for parameter values Ξ± = ( 2 ⁒ n + 1 ) / 2 , n = 0 , … , 5 . Angew. Informatik 17, pp. 30–32.
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    Notes:
    Includes Fortran code.
    External Links:
    ZentralBlatt
    Referenced by:
    §8.28(ii).
    Encodings:
    BibTeX
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  • H. M. Srivastava and J. Choi (2001) Series Associated with the Zeta and Related Functions. Kluwer Academic Publishers, Dordrecht.
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    External Links:
    ISBN 0-7923-7054-6, MathReview (Richard B. Paris), ZentralBlatt
    Referenced by:
    (25.11.25), (25.11.8), §25.11, §25.11(iv), §25.11(x), (25.8.9), §25.8.
    Encodings:
    BibTeX
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  • H. M. Srivastava (1988) Sums of certain series of the Riemann zeta function. J. Math. Anal. Appl. 134 (1), pp. 129–140.
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    External Links:
    ISSN 0022-247X, Document, MathReview (Aleksandar Ivić), ZentralBlatt
    Referenced by:
    (25.8.3), §25.8.
    Encodings:
    BibTeX
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    16: Bibliography M
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  • I. G. Macdonald (1990) Hypergeometric Functions.
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    Notes:
    Unpublished Lecture Notes, University of London. An online version exists.
    External Links:
    FullText
    Referenced by:
    §35.7(ii), §35.8(iii).
    Encodings:
    BibTeX
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  • K. L. Majumder and G. P. Bhattacharjee (1973) Algorithm AS 63. The incomplete beta integral. Appl. Statist. 22 (3), pp. 409–411.
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    Notes:
    Double-precision Fortran. For remark see same journal 26 (1977), pp. 111-114
    External Links:
    FullText, Code
    Referenced by:
    4th item.
    Encodings:
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  • B. Markman (1965) Contribution no. 14. The Riemann zeta function. BIT 5, pp. 138–141.
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    Referenced by:
    §25.21(ii).
    Encodings:
    BibTeX
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  • J. Miller and V. S. Adamchik (1998) Derivatives of the Hurwitz zeta function for rational arguments. J. Comput. Appl. Math. 100 (2), pp. 201–206.
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    External Links:
    ISSN 0377-0427, Document, MathReview, ZentralBlatt
    Referenced by:
    (25.11.21), (25.11.22), (25.11.23), §25.11, §25.11(vi), §25.18(i), (25.6.15).
    Encodings:
    BibTeX
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  • R. J. Moore (1982) Algorithm AS 187. Derivatives of the incomplete gamma integral. Appl. Statist. 31 (3), pp. 330–335.
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    Notes:
    Single-precision Fortran.
    External Links:
    FullText, Code, Document, ZentralBlatt
    Referenced by:
    4th item.
    Encodings:
    BibTeX
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    17: 19.25 Relations to Other Functions
    §19.25 Relations to Other Functions
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    §19.25(iv) Theta Functions
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    §19.25(v) Jacobian Elliptic Functions
    … β–Ί … β–Ίin which 2 ⁒ Ο‰ 1 and 2 ⁒ Ο‰ 3 are generators for the lattice 𝕃 , Ο‰ 2 = − Ο‰ 1 − Ο‰ 3 , and Ξ· j = ΞΆ ⁑ ( Ο‰ j ) (see (23.2.12)). …
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