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1: DLMF Project News
error generating summary
2: Foreword
However, we have also seen the birth of a new age of computing technology, which has not only changed how we utilize special functions, but also how we communicate technical information. …
3: Frank W. J. Olver
Having witnessed the birth of the computer age firsthand (as a colleague of Alan Turing at NPL, for example), Olver is also well known for his contributions to the development and analysis of numerical methods for computing special functions. … He continued his editing work until the time of his death on April 22, 2013 at age 88.
4: Publications
  • R. Boisvert, C. W. Clark, D. Lozier and F. Olver (2011) A Special Functions Handbook for the Digital Age, Notices of the American Mathematical Society 58, 7 (2011), pp. 905–911. PDF
  • 5: 30.17 Tables
  • Hanish et al. (1970) gives λ n m ( γ 2 ) and S n m ( j ) ( z , γ ) , j = 1 , 2 , and their first derivatives, for 0 m 2 , m n m + 49 , 1600 γ 2 1600 . The range of z is given by 1 z 10 if γ 2 > 0 , or z = i ξ , 0 ξ 2 if γ 2 < 0 . Precision is 18S.

  • Van Buren et al. (1975) gives λ n 0 ( γ 2 ) , 𝖯𝗌 n 0 ( x , γ 2 ) for 0 n 49 , 1600 γ 2 1600 , 1 x 1 . Precision is 8S.

  • 6: 26.2 Basic Definitions
    Table 26.2.1: Partitions p ( n ) .
    n p ( n ) n p ( n ) n p ( n )
    15 176 32 8349 49 1 73525
    7: Bibliography U
  • F. Ursell (1972) Integrals with a large parameter. Several nearly coincident saddle-points. Proc. Cambridge Philos. Soc. 72, pp. 49–65.
  • 8: Bibliography Y
  • F. L. Yost, J. A. Wheeler, and G. Breit (1936) Coulomb wave functions in repulsive fields. Phys. Rev. 49 (2), pp. 174–189.
  • 9: 35.1 Special Notation
    Related notations for the Bessel functions are 𝒥 ν + 1 2 ( m + 1 ) ( 𝐓 ) = A ν ( 𝐓 ) / A ν ( 𝟎 ) (Faraut and Korányi (1994, pp. 320–329)), K m ( 0 , , 0 , ν | 𝐒 , 𝐓 ) = | 𝐓 | ν B ν ( 𝐒 𝐓 ) (Terras (1988, pp. 49–64)), and 𝒦 ν ( 𝐓 ) = | 𝐓 | ν B ν ( 𝐒 𝐓 ) (Faraut and Korányi (1994, pp. 357–358)).
    10: 6.14 Integrals