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1: 20.12 Mathematical Applications
For applications of θ 3 ( 0 , q ) to problems involving sums of squares of integers see §27.13(iv), and for extensions see Estermann (1959), Serre (1973, pp. 106–109), Koblitz (1993, pp. 176–177), and McKean and Moll (1999, pp. 142–143). …
2: 10.65 Power Series
§10.65(iii) Cross-Products and Sums of Squares
3: 22.6 Elementary Identities
§22.6(i) Sums of Squares
4: 10.67 Asymptotic Expansions for Large Argument
§10.67(ii) Cross-Products and Sums of Squares in the Case ν = 0
5: 20.7 Identities
§20.7(i) Sums of Squares
6: Bibliography M
  • S. C. Milne (2002) Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions. Ramanujan J. 6 (1), pp. 7–149.
  • S. C. Milne (1996) New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function. Proc. Nat. Acad. Sci. U.S.A. 93 (26), pp. 15004–15008.
  • L. J. Mordell (1917) On the representation of numbers as a sum of 2 r squares. Quarterly Journal of Math. 48, pp. 93–104.
  • 7: 10.49 Explicit Formulas
    §10.49(iv) Sums or Differences of Squares
    8: Guide to Searching the DLMF
    Table 1: Query Examples
    Query

    Matching records contain

    trigonometric^2 + trig$^2

    any sum of the squares of two trigonometric functions such as sin 2 z + cos 2 z .

    9: Bibliography E
  • T. Estermann (1959) On the representations of a number as a sum of three squares. Proc. London Math. Soc. (3) 9, pp. 575–594.
  • 10: Bibliography G
  • E. Grosswald (1985) Representations of Integers as Sums of Squares. Springer-Verlag, New York.