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1: DLMF Project News
error generating summary
2: Publications
  • R. F. Boisvert and D. W. Lozier (2001) Handbook of Mathematical Functions, in A Century of Excellence in Measurements Standards and Technology (D. R. Lide, ed.), CRC Press, pp. 135–139. PDF
  • 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
  • 3: 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. …
    4: 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.
    5: 7 Error Functions, Dawson’s and Fresnel Integrals
    Chapter 7 Error Functions, Dawson’s and Fresnel Integrals
    6: 23 Weierstrass Elliptic and Modular
    Functions
    7: 9.4 Maclaurin Series
    9.4.1 Ai ( z ) = Ai ( 0 ) ( 1 + 1 3 ! z 3 + 1 4 6 ! z 6 + 1 4 7 9 ! z 9 + ) + Ai ( 0 ) ( z + 2 4 ! z 4 + 2 5 7 ! z 7 + 2 5 8 10 ! z 10 + ) ,
    9.4.2 Ai ( z ) = Ai ( 0 ) ( 1 + 2 3 ! z 3 + 2 5 6 ! z 6 + 2 5 8 9 ! z 9 + ) + Ai ( 0 ) ( 1 2 ! z 2 + 1 4 5 ! z 5 + 1 4 7 8 ! z 8 + ) ,
    9.4.3 Bi ( z ) = Bi ( 0 ) ( 1 + 1 3 ! z 3 + 1 4 6 ! z 6 + 1 4 7 9 ! z 9 + ) + Bi ( 0 ) ( z + 2 4 ! z 4 + 2 5 7 ! z 7 + 2 5 8 10 ! z 10 + ) ,
    9.4.4 Bi ( z ) = Bi ( 0 ) ( 1 + 2 3 ! z 3 + 2 5 6 ! z 6 + 2 5 8 9 ! z 9 + ) + Bi ( 0 ) ( 1 2 ! z 2 + 1 4 5 ! z 5 + 1 4 7 8 ! z 8 + ) .
    8: 16.25 Methods of Computation
    See §§3.6(vii), 3.7(iii), Olde Daalhuis and Olver (1998), Lozier (1980), and Wimp (1984, Chapters 7, 8).
    9: 25 Zeta and Related Functions
    10: 26.13 Permutations: Cycle Notation
    26.13.2 [ 1 2 3 4 5 6 7 8 3 5 2 4 7 8 1 6 ]
    is ( 1 , 3 , 2 , 5 , 7 ) ( 4 ) ( 6 , 8 ) in cycle notation. …In consequence, (26.13.2) can also be written as ( 1 , 3 , 2 , 5 , 7 ) ( 6 , 8 ) . … For the example (26.13.2), this decomposition is given by ( 1 , 3 , 2 , 5 , 7 ) ( 6 , 8 ) = ( 1 , 3 ) ( 2 , 3 ) ( 2 , 5 ) ( 5 , 7 ) ( 6 , 8 ) . Again, for the example (26.13.2) a minimal decomposition into adjacent transpositions is given by ( 1 , 3 , 2 , 5 , 7 ) ( 6 , 8 ) = ( 2 , 3 ) ( 1 , 2 ) ( 4 , 5 ) ( 3 , 4 ) ( 2 , 3 ) ( 3 , 4 ) ( 4 , 5 ) ( 6 , 7 ) ( 5 , 6 ) ( 7 , 8 ) ( 6 , 7 ) : inv ( ( 1 , 3 , 2 , 5 , 7 ) ( 6 , 8 ) ) = 11 .