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1: 27.17 Other Applications
Apostol and Zuckerman (1951) uses congruences to construct magic squares. …
2: 27.13 Functions
The basic problem is that of expressing a given positive integer n as a sum of integers from some prescribed set S whose members are primes, squares, cubes, or other special integers. …
§27.13(iv) Representation by Squares
For a given integer k 2 the function r k ( n ) is defined as the number of solutions of the equation … Jacobi (1829) notes that r 2 ( n ) is the coefficient of x n in the square of the theta function ϑ ( x ) : … For more than 8 squares, Milne’s identities are not the same as those obtained earlier by Mordell and others.
3: 8.23 Statistical Applications
§8.23 Statistical Applications
Particular forms are the chi-square distribution functions; see Johnson et al. (1994, pp. 415–493). …
4: 19.38 Approximations
Approximations for Legendre’s complete or incomplete integrals of all three kinds, derived by Padé approximation of the square root in the integrand, are given in Luke (1968, 1970). …
5: 27.22 Software
  • Maple. isprime combines a strong pseudoprime test and a Lucas pseudoprime test. ifactor uses cfrac27.19) after exhausting trial division. Brent–Pollard rho, Square Forms Factorization, and ecm are available also; see §27.19.

  • 6: 34.14 Tables
    Tables of exact values of the squares of the 3 j and 6 j symbols in which all parameters are 8 are given in Rotenberg et al. (1959), together with a bibliography of earlier tables of 3 j , 6 j , and 9 j symbols on pp. …
    7: 18.36 Miscellaneous Polynomials
    These are matrix-valued polynomials that are orthogonal with respect to a square matrix of measures on the real line. …
    8: 3.11 Approximation Techniques
    §3.11(v) Least Squares Approximations
    For further information on least squares approximations, including examples, see Gautschi (1997a, Chapter 2) and Björck (1996, Chapters 1 and 2). …
    9: 19.31 Probability Distributions
    R G ( x , y , z ) and R F ( x , y , z ) occur as the expectation values, relative to a normal probability distribution in 2 or 3 , of the square root or reciprocal square root of a quadratic form. …
    10: 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). …