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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: 1.1 Special Notation
x , y real variables.
L 2 ( X , d α ) the space of all Lebesgue–Stieltjes measurable functions on X which are square integrable with respect to d α .
𝐀 1 inverse of the square matrix 𝐀
det ( 𝐀 ) determinant of the square matrix 𝐀
tr ( 𝐀 ) trace of the square matrix 𝐀
𝐀 adjoint of the square matrix 𝐀
4: 8.23 Statistical Applications
§8.23 Statistical Applications
Particular forms are the chi-square distribution functions; see Johnson et al. (1994, pp. 415–493). …
5: 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). …
6: 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.

  • 7: 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. …
    8: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
    §1.18(ii) L 2 spaces on intervals in
    For a Lebesgue–Stieltjes measure d α on X let L 2 ( X , d α ) be the space of all Lebesgue–Stieltjes measurable complex-valued functions on X which are square integrable with respect to d α , …The space L 2 ( X , d α ) becomes a separable Hilbert space with inner product … Eigenfunctions corresponding to the continuous spectrum are non- L 2 functions. … The well must be deep and broad enough to allow existence of such L 2 discrete states. …
    9: 1.2 Elementary Algebra
    §1.2(vi) Square Matrices
    Special Forms of Square Matrices
    Norms of Square Matrices
    Non-Defective Square Matrices
    10: 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). …