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1: 1.17 Integral and Series Representations of the Dirac Delta
§1.17(iv) Mathematical Definitions
2: Errata
  • Changes


    • In Paragraph Inversion Formula in §35.2, the wording was changed to make the integration variable more apparent.

    • In many cases, the links from mathematical symbols to their definitions were corrected or improved. These links were also enhanced with ‘tooltip’ feedback, where supported by the user’s browser.

  • 3: DLMF Project News
    error generating summary
    4: Preface
    The Web pages contain many active links, for example, to the definitions of symbols within the DLMF, and to external sources of reviews, full texts of articles, and items of mathematical software. …
    5: Foreword
    In 1964 the National Institute of Standards and Technology11 1 Then known as the National Bureau of Standards. published the Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, edited by Milton Abramowitz and Irene A. … Certainly, advances in applied mathematics have continued unabated. …The new printed volume, the NIST Handbook of Mathematical Functions, serves a similar function as the original A&S, though it is heavily updated and extended. The online version, the NIST Digital Library of Mathematical Functions (DLMF), presents the same technical information along with extensions and innovative interactive features consistent with the new medium. The DLMF may well serve as a model for the effective presentation of highly mathematical reference material on the Web. …
    6: Need Help?
    In the Digital Library of Mathematical Functions, we have tried to provide the most accurate, carefully selected information about Special Functions possible. …
  • Mathematics

  • Finding Things

    • How do I search within DLMF? See Guide to Searching the DLMF.

    • See also the Index or Notations sections.

    • Links to definitions, keywords, annotations and other interesting information can be found in the Info boxes by clicking or hovering the mouse over the icon next to each formula, table, figure, and section heading.

  • 7: Mathematical Introduction
    Mathematical Introduction
    The mathematical content of the NIST Handbook of Mathematical Functions has been produced over a ten-year period. …
    Common Notations and Definitions
    His genius in the creation of the National Bureau of Standards Handbook of Mathematical Functions paid enormous dividends to the world’s scientific, mathematical, and engineering communities, and paved the way for the development of the NIST Handbook of Mathematical Functions and NIST Digital Library of Mathematical Functions. …  Olver, Mathematics Editor
    8: 25.16 Mathematical Applications
    §25.16 Mathematical Applications
    25.16.1 ψ ( x ) = m = 1 p m x ln p ,
    9: 14.30 Spherical and Spheroidal Harmonics
    §14.30(i) Definitions
    Sometimes Y l , m ( θ , ϕ ) is denoted by i - l 𝔇 l m ( θ , ϕ ) ; also the definition of Y l , m ( θ , ϕ ) can differ from (14.30.1), for example, by inclusion of a factor ( - 1 ) m . … Most mathematical properties of Y l , m ( θ , ϕ ) can be derived directly from (14.30.1) and the properties of the Ferrers function of the first kind given earlier in this chapter. …
    14.30.4 Y l , m ( 0 , ϕ ) = { ( 2 l + 1 4 π ) 1 / 2 , m = 0 , 0 , | m | = 1 , 2 , 3 , ,
    10: Bibliography R
  • J. Raynal (1979) On the definition and properties of generalized 6 - j  symbols. J. Math. Phys. 20 (12), pp. 2398–2415.
  • D. St. P. Richards (Ed.) (1992) Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications. Contemporary Mathematics, Vol. 138, American Mathematical Society, Providence, RI.
  • K. H. Rosen, J. G. Michaels, J. L. Gross, J. W. Grossman, and D. R. Shier (Eds.) (2000) Handbook of Discrete and Combinatorial Mathematics. CRC Press, Boca Raton, FL.
  • W. Rudin (1973) Functional Analysis. McGraw-Hill Book Co., New York.
  • W. Rudin (1976) Principles of Mathematical Analysis. 3rd edition, McGraw-Hill Book Co., New York.