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1: Guide to Searching the DLMF
  • All the Greek Letters (gamma vs. Gamma, sigma vs. Sigma, etc.)

  • All the inverse trigonometric functions (arcsin vs. Arcsin, etc.).

  • Sometimes there are distinctions between various special function names based on font style, such as the use of bold or calligraphic letters. DLMF search recognizes just the essential font differences, that is, the font style differences deemed important for the DLMF contents: … If you don’t specify the font style or font accessories in the query, the style and accessories won’t matter in the search, but if you specify them, they will matter. …
    2: Staff
  • Richard A. Askey, University of Wisconsin, Chaps. 1, 5, 16

  • Richard B. Paris, University of Abertay, Chaps. 8, 11

  • Hans Volkmer, University of Wisconsin, Milwaukee, Chaps. 29, 30

  • Richard B. Paris, University of Abertay Dundee, for Chaps. 8, 11 (deceased)

  • Hans Volkmer, University of Wisconsin–Milwaukee, for Chaps. 29, 30

  • 3: 24.2 Definitions and Generating Functions
    Table 24.2.3: Bernoulli numbers B n = N / D .
    n N D B n
    30 861 58412 76005 14322 6.01580 8739 ×10⁸
    Table 24.2.4: Euler numbers E n .
    n E n
    30 44 15438 93249 02310 45536 82821
    Table 24.2.5: Coefficients b n , k of the Bernoulli polynomials B n ( x ) = k = 0 n b n , k x k .
    k
    n 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
    11 0 5 6 0 11 2 0 11 0 11 0 55 6 11 2 1
    Table 24.2.6: Coefficients e n , k of the Euler polynomials E n ( x ) = k = 0 n e n , k x k .
    k
    n 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
    4: 26.2 Basic Definitions
    Table 26.2.1: Partitions p ( n ) .
    n p ( n ) n p ( n ) n p ( n )
    6 11 23 1255 40 37338
    9 30 26 2436 43 63261
    11 56 28 3718 45 89134
    13 101 30 5604 47 1 24754
    16 231 33 10143 50 2 04226
    5: 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) Advances in Math Search, Proceedings 6th International Congress on Industrial and Applied Mathematics, Zürich, Switzerland, July 17, 2007. 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
  • 6: 11 Struve and Related Functions
    Chapter 11 Struve and Related Functions
    7: Bibliography Y
  • A. I. Yablonskiĭ (1959) On rational solutions of the second Painlevé equation. Vesti Akad. Navuk. BSSR Ser. Fiz. Tkh. Nauk. 3, pp. 30–35 (Russian).
  • H. A. Yamani and L. Fishman (1975) J -matrix method: Extensions to arbitrary angular momentum and to Coulomb scattering. J. Math. Phys. 16, pp. 410–420.
  • H. A. Yamani and W. P. Reinhardt (1975) L -squared discretizations of the continuum: Radial kinetic energy and the Coulomb Hamiltonian. Phys. Rev. A 11 (4), pp. 1144–1156.
  • 8: 13.30 Tables
  • Slater (1960) tabulates M ( a , b , x ) for a = 1 ( .1 ) 1 , b = 0.1 ( .1 ) 1 , and x = 0.1 ( .1 ) 10 , 7–9S; M ( a , b , 1 ) for a = 11 ( .2 ) 2 and b = 4 ( .2 ) 1 , 7D; the smallest positive x -zero of M ( a , b , x ) for a = 4 ( .1 ) 0.1 and b = 0.1 ( .1 ) 2.5 , 7D.

  • Zhang and Jin (1996, pp. 411–423) tabulates M ( a , b , x ) and U ( a , b , x ) for a = 5 ( .5 ) 5 , b = 0.5 ( .5 ) 5 , and x = 0.1 , 1 , 5 , 10 , 20 , 30 , 8S (for M ( a , b , x ) ) and 7S (for U ( a , b , x ) ).

  • 9: 27.2 Functions
    Table 27.2.1: Primes.
    n p n p n + 10 p n + 20 p n + 30 p n + 40 p n + 50 p n + 60 p n + 70 p n + 80 p n + 90
    5 11 47 97 149 197 257 313 379 439 499
    Table 27.2.2: Functions related to division.
    n ϕ ( n ) d ( n ) σ ( n ) n ϕ ( n ) d ( n ) σ ( n ) n ϕ ( n ) d ( n ) σ ( n ) n ϕ ( n ) d ( n ) σ ( n )
    3 2 2 4 16 8 5 31 29 28 2 30 42 12 8 96
    4 2 3 7 17 16 2 18 30 8 8 72 43 42 2 44
    5 4 2 6 18 6 6 39 31 30 2 32 44 20 6 84
    11 10 2 12 24 8 8 60 37 36 2 38 50 20 6 93
    10: 26.9 Integer Partitions: Restricted Number and Part Size
    Table 26.9.1: Partitions p k ( n ) .
    n k
    6 0 1 4 7 9 10 11 11 11 11 11
    7 0 1 4 8 11 13 14 15 15 15 15
    9 0 1 5 12 18 23 26 28 29 30 30
    10 0 1 6 14 23 30 35 38 40 41 42