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1: Publications
  • B. V. Saunders and Q. Wang (2005) Boundary/Contour Fitted Grid Generation for Effective Visualizations in a Digital Library of Mathematical Functions, Proceedings of the 9th International Conference on Numerical Grid Generation in Computational Field Simulations, San Jose, June 11–18, 2005. pp. 61–71. PDF
  • Q. Wang and B. V. Saunders (2005) Web-Based 3D Visualization in a Digital Library of Mathematical Functions, Proceedings of the Web3D Symposium, Bangor, UK, March 29–April 1, 2005. PDF
  • A. Youssef (2007) Methods of Relevance Ranking and Hit-content Generation in Math Search, Proceedings of Mathematical Knowledge Management (MKM2007), RISC, Hagenberg, Austria, June 27–30, 2007. PDF
  • B. I. Schneider, B. R. Miller and B. V. Saunders (2018) NIST’s Digital Library of Mathematial Functions, Physics Today 71, 2, 48 (2018), pp. 48–53. PDF
  • 2: DLMF Project News
    error generating summary
    3: Bibliography N
  • G. Nemes (2018) Error bounds for the large-argument asymptotic expansions of the Lommel and allied functions. Stud. Appl. Math. 140 (4), pp. 508–541.
  • E. Neuman (1969a) Elliptic integrals of the second and third kinds. Zastos. Mat. 11, pp. 99–102.
  • E. Neuman (1969b) On the calculation of elliptic integrals of the second and third kinds. Zastos. Mat. 11, pp. 91–94.
  • V. Yu. Novokshënov (1985) The asymptotic behavior of the general real solution of the third Painlevé equation. Dokl. Akad. Nauk SSSR 283 (5), pp. 1161–1165 (Russian).
  • 4: 27.12 Asymptotic Formulas: Primes
    p n is the n th prime, beginning with p 1 = 2 . …
    27.12.1 lim n p n n ln n = 1 ,
    27.12.2 p n > n ln n , n = 1 , 2 , .
    27.12.3 π ( x ) = x 1 p j x x p j + r 2 ( 1 ) r p j 1 < p j 2 < < p j r x x p j 1 p j 2 p j r , x 1 ,
    The largest known prime (2018) is the Mersenne prime 2 82 , 589 , 933 1 . …
    5: Bibliography I
  • IEEE (2018) IEEE Standard for Interval Arithmetic: IEEE Std 1788.1-2017. The Institute of Electrical and Electronics Engineers, Inc..
  • Y. Ikebe, Y. Kikuchi, I. Fujishiro, N. Asai, K. Takanashi, and M. Harada (1993) The eigenvalue problem for infinite compact complex symmetric matrices with application to the numerical computation of complex zeros of J 0 ( z ) i J 1 ( z ) and of Bessel functions J m ( z ) of any real order m . Linear Algebra Appl. 194, pp. 35–70.
  • 6: 3.1 Arithmetics and Error Measures
    where s is equal to 1 or 0 , each b j , j 1 , is either 0 or 1 , b 1 is the most significant bit, p ( ) is the number of significant bits b j , b p 1 is the least significant bit, E is an integer called the exponent, b 0 . b 1 b 2 b p 1 is the significand, and f = . b 1 b 2 b p 1 is the fractional part. … with b 0 = 1 and all allowable choices of E , p , s , and b j . … Let E min E E max with E min < 0 and E max > 0 . … The respective machine precisions are 1 2 ϵ M = 0.596 × 10 7 , 1 2 ϵ M = 0.111 × 10 15 and 1 2 ϵ M = 0.963 × 10 34 . … For interval arithmetic, one should refer to the IEEE Standards for Interval Arithmetic IEEE (2015, 2018). …
    7: Bibliography O
  • K. Okamoto (1987c) Studies on the Painlevé equations. IV. Third Painlevé equation P III . Funkcial. Ekvac. 30 (2-3), pp. 305–332.
  • S. Olver (2011) Numerical solution of Riemann-Hilbert problems: Painlevé II. Found. Comput. Math. 11 (2), pp. 153–179.
  • M. Onoe (1956) Modified quotients of cylinder functions. Math. Tables Aids Comput. 10, pp. 27–28.
  • G. E. Ordóñez and D. J. Driebe (1996) Spectral decomposition of tent maps using symmetry considerations. J. Statist. Phys. 84 (1-2), pp. 269–276.
  • H. Oser (1960) Algorithm 22: Riccati-Bessel functions of first and second kind. Comm. ACM 3 (11), pp. 600–601.
  • 8: Errata
  • Paragraph Prime Number Theorem (in §27.12)

    The largest known prime, which is a Mersenne prime, was updated from 2 43 , 112 , 609 1 (2009) to 2 82 , 589 , 933 1 (2018).

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    9: 11 Struve and Related Functions
    Chapter 11 Struve and Related Functions
    10: 11.11 Asymptotic Expansions of Anger–Weber Functions
    Let F 0 ( ν ) = G 0 ( ν ) = 1 , and for k = 1 , 2 , 3 , , …For sharp error bounds and exponentially-improved extensions, see Nemes (2018). … where … and …with the U k defined in §10.41(ii). …