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1: 5.10 Continued Fractions
a 1 = 1 30 ,
a 2 = 53 210 ,
For exact values of a 7 to a 11 and 40S values of a 0 to a 40 , see Char (1980). …
2: 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
  • 3: 11 Struve and Related Functions
    Chapter 11 Struve and Related Functions
    4: 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 ) ).

  • 5: 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
    6: 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
    7: Staff
  • 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

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

  • 8: 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
    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: Bibliography
  • M. Abramowitz (1949) Asymptotic expansions of spheroidal wave functions. J. Math. Phys. Mass. Inst. Tech. 28, pp. 195–199.
  • S. Ahmed and M. E. Muldoon (1980) On the zeros of confluent hypergeometric functions. III. Characterization by means of nonlinear equations. Lett. Nuovo Cimento (2) 29 (11), pp. 353–358.
  • V. I. Arnol’d (1974) Normal forms of functions in the neighborhood of degenerate critical points. Uspehi Mat. Nauk 29 (2(176)), pp. 11–49 (Russian).
  • V. I. Arnol’d (1975) Critical points of smooth functions, and their normal forms. Uspehi Mat. Nauk 30 (5(185)), pp. 3–65 (Russian).
  • R. Askey (1980) Some basic hypergeometric extensions of integrals of Selberg and Andrews. SIAM J. Math. Anal. 11 (6), pp. 938–951.