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1: Staff
  • Frank W. J. Olver, University of Maryland and NIST, Chaps. 1, 2, 4, 9, 10

  • 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

  • 2: Publications
  • D. W. Lozier, B. R. Miller and B. V. Saunders (1999) Design of a Digital Mathematical Library for Science, Technology and Education, Proceedings of the IEEE Forum on Research and Technology Advances in Digital Libraries (IEEE ADL ’99, Baltimore, Maryland, May 19, 1999). PDF
  • 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
  • B. V. Saunders and Q. Wang (2006) From B-Spline Mesh Generation to Effective Visualizations for the NIST Digital Library of Mathematical Functions, in Curve and Surface Design, Proceedings of the Sixth International Conference on Curves and Surfaces, Avignon, France June 29–July 5, 2006, pp. 235–243. 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: 10 Bessel Functions
    4: 34.6 Definition: 9 j Symbol
    34.6.1 { j 11 j 12 j 13 j 21 j 22 j 23 j 31 j 32 j 33 } = all  m r s ( j 11 j 12 j 13 m 11 m 12 m 13 ) ( j 21 j 22 j 23 m 21 m 22 m 23 ) ( j 31 j 32 j 33 m 31 m 32 m 33 ) ( j 11 j 21 j 31 m 11 m 21 m 31 ) ( j 12 j 22 j 32 m 12 m 22 m 32 ) ( j 13 j 23 j 33 m 13 m 23 m 33 ) ,
    34.6.2 { j 11 j 12 j 13 j 21 j 22 j 23 j 31 j 32 j 33 } = j ( 1 ) 2 j ( 2 j + 1 ) { j 11 j 21 j 31 j 32 j 33 j } { j 12 j 22 j 32 j 21 j j 23 } { j 13 j 23 j 33 j j 11 j 12 } .
    5: 26.2 Basic Definitions
    Thus 231 is the permutation σ ( 1 ) = 2 , σ ( 2 ) = 3 , σ ( 3 ) = 1 . … Here σ ( 1 ) = 2 , σ ( 2 ) = 5 , and σ ( 5 ) = 1 . … A lattice path is a directed path on the plane integer lattice { 0 , 1 , 2 , } × { 0 , 1 , 2 , } . … As an example, { 1 , 3 , 4 } , { 2 , 6 } , { 5 } is a partition of { 1 , 2 , 3 , 4 , 5 , 6 } . … As an example, { 1 , 1 , 1 , 2 , 4 , 4 } is a partition of 13. …
    6: 4.17 Special Values and Limits
    Table 4.17.1: Trigonometric functions: values at multiples of 1 12 π .
    θ sin θ cos θ tan θ csc θ sec θ cot θ
    π / 4 1 2 2 1 2 2 1 2 2 1
    2 π / 3 1 2 3 1 2 3 2 3 3 2 1 3 3
    3 π / 4 1 2 2 1 2 2 1 2 2 1
    11 π / 12 1 4 2 ( 3 1 ) 1 4 2 ( 3 + 1 ) ( 2 3 ) 2 ( 3 + 1 ) 2 ( 3 1 ) ( 2 + 3 )
    4.17.3 lim z 0 1 cos z z 2 = 1 2 .
    7: 11 Struve and Related Functions
    Chapter 11 Struve and Related Functions
    8: 26.9 Integer Partitions: Restricted Number and Part Size
    Figure 26.9.1: Ferrers graph of the partition 7 + 4 + 3 + 3 + 2 + 1 .
    The conjugate to the example in Figure 26.9.1 is 6 + 5 + 4 + 2 + 1 + 1 + 1 . …
    Figure 26.9.2: The partition 5 + 5 + 3 + 2 represented as a lattice path.
    p 2 ( n ) = 1 + n / 2 ,
    p 3 ( n ) = 1 + n 2 + 6 n 12 .
    9: 34.7 Basic Properties: 9 j Symbol
    34.7.1 { j 11 j 12 j 13 j 21 j 22 j 13 j 31 j 31 0 } = ( 1 ) j 12 + j 21 + j 13 + j 31 ( ( 2 j 13 + 1 ) ( 2 j 31 + 1 ) ) 1 2 { j 11 j 12 j 13 j 22 j 21 j 31 } .
    34.7.2 j 12 j 34 ( 2 j 12 + 1 ) ( 2 j 34 + 1 ) ( 2 j 13 + 1 ) ( 2 j 24 + 1 ) { j 1 j 2 j 12 j 3 j 4 j 34 j 13 j 24 j } { j 1 j 2 j 12 j 3 j 4 j 34 j 13 j 24 j } = δ j 13 , j 13 δ j 24 , j 24 .
    34.7.3 j 13 j 24 ( 1 ) 2 j 2 + j 24 + j 23 j 34 ( 2 j 13 + 1 ) ( 2 j 24 + 1 ) { j 1 j 2 j 12 j 3 j 4 j 34 j 13 j 24 j } { j 1 j 3 j 13 j 4 j 2 j 24 j 14 j 23 j } = { j 1 j 2 j 12 j 4 j 3 j 34 j 14 j 23 j } .
    34.7.4 ( j 13 j 23 j 33 m 13 m 23 m 33 ) { j 11 j 12 j 13 j 21 j 22 j 23 j 31 j 32 j 33 } = m r 1 , m r 2 , r = 1 , 2 , 3 ( j 11 j 12 j 13 m 11 m 12 m 13 ) ( j 21 j 22 j 23 m 21 m 22 m 23 ) ( j 31 j 32 j 33 m 31 m 32 m 33 ) ( j 11 j 21 j 31 m 11 m 21 m 31 ) ( j 12 j 22 j 32 m 12 m 22 m 32 ) .
    34.7.5 j ( 2 j + 1 ) { j 11 j 12 j j 21 j 22 j 23 j 31 j 32 j 33 } { j 11 j 12 j j 23 j 33 j } = ( 1 ) 2 j { j 21 j 22 j 23 j 12 j j 32 } { j 31 j 32 j 33 j j 11 j 21 } .
    10: 29 Lamé Functions
    Chapter 29 Lamé Functions