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1: 26.21 Tables
§26.21 Tables
Abramowitz and Stegun (1964, Chapter 24) tabulates binomial coefficients ( m n ) for m up to 50 and n up to 25; extends Table 26.4.1 to n = 10 ; tabulates Stirling numbers of the first and second kinds, s ( n , k ) and S ( n , k ) , for n up to 25 and k up to n ; tabulates partitions p ( n ) and partitions into distinct parts p ( 𝒟 , n ) for n up to 500. … Goldberg et al. (1976) contains tables of binomial coefficients to n = 100 and Stirling numbers to n = 40 .
2: 26.3 Lattice Paths: Binomial Coefficients
Table 26.3.1: Binomial coefficients ( m n ) .
m n
Table 26.3.2: Binomial coefficients ( m + n m ) for lattice paths.
m n
3: 28.35 Tables
§28.35 Tables
  • Ince (1932) includes eigenvalues a n , b n , and Fourier coefficients for n = 0 or 1 ( 1 ) 6 , q = 0 ( 1 ) 10 ( 2 ) 20 ( 4 ) 40 ; 7D. Also ce n ( x , q ) , se n ( x , q ) for q = 0 ( 1 ) 10 , x = 1 ( 1 ) 90 , corresponding to the eigenvalues in the tables; 5D. Notation: a n = 𝑏𝑒 n 2 q , b n = 𝑏𝑜 n 2 q .

  • National Bureau of Standards (1967) includes the eigenvalues a n ( q ) , b n ( q ) for n = 0 ( 1 ) 3 with q = 0 ( .2 ) 20 ( .5 ) 37 ( 1 ) 100 , and n = 4 ( 1 ) 15 with q = 0 ( 2 ) 100 ; Fourier coefficients for ce n ( x , q ) and se n ( x , q ) for n = 0 ( 1 ) 15 , n = 1 ( 1 ) 15 , respectively, and various values of q in the interval [ 0 , 100 ] ; joining factors g e , n ( q ) , f e , n ( q ) for n = 0 ( 1 ) 15 with q = 0 ( .5  to  10 ) 100 (but in a different notation). Also, eigenvalues for large values of q . Precision is generally 8D.

  • Blanch and Clemm (1969) includes eigenvalues a n ( q ) , b n ( q ) for q = ρ e i ϕ , ρ = 0 ( .5 ) 25 , ϕ = 5 ( 5 ) 90 , n = 0 ( 1 ) 15 ; 4D. Also a n ( q ) and b n ( q ) for q = i ρ , ρ = 0 ( .5 ) 100 , n = 0 ( 2 ) 14 and n = 2 ( 2 ) 16 , respectively; 8D. Double points for n = 0 ( 1 ) 15 ; 8D. Graphs are included.

  • 4: 18.3 Definitions
    Table 18.3.1: Orthogonality properties for classical OP’s: intervals, weight functions, standardizations, leading coefficients, and parameter constraints. …
    Name p n ( x ) ( a , b ) w ( x ) h n k n k ~ n / k n Constraints
    For explicit power series coefficients up to n = 12 for these polynomials and for coefficients up to n = 6 for Jacobi and ultraspherical polynomials see Abramowitz and Stegun (1964, pp. 793–801). …
    5: 26.4 Lattice Paths: Multinomial Coefficients and Set Partitions
    Table 26.4.1: Multinomials and partitions.
    n m λ M 1 M 2 M 3
    6: 30.17 Tables
    §30.17 Tables
  • Flammer (1957) includes 18 tables of eigenvalues, expansion coefficients, spheroidal wave functions, and other related quantities. Precision varies between 4S and 10S.

  • 7: 18.25 Wilson Class: Definitions
    Table 18.25.2 provides the leading coefficients k n 18.2(iii)) for the Wilson, continuous dual Hahn, Racah, and dual Hahn polynomials.
    Table 18.25.2: Wilson class OP’s: leading coefficients.
    p n ( x ) k n
    8: 18.19 Hahn Class: Definitions
    Table 18.19.2: Hahn, Krawtchouk, Meixner, and Charlier OP’s: leading coefficients.
    p n ( x ) k n
    9: 25.19 Tables
  • Cloutman (1989) tabulates Γ ( s + 1 ) F s ( x ) , where F s ( x ) is the Fermi–Dirac integral (25.12.14), for s = 1 2 , 1 2 , 3 2 , 5 2 , x = 5 ( .05 ) 25 , to 12S.

  • Fletcher et al. (1962, §22.1) lists many sources for earlier tables of ζ ( s ) for both real and complex s . §22.133 gives sources for numerical values of coefficients in the Riemann–Siegel formula, §22.15 describes tables of values of ζ ( s , a ) , and §22.17 lists tables for some Dirichlet L -functions for real characters. For tables of dilogarithms, polylogarithms, and Clausen’s integral see §§22.84–22.858.

  • 10: 24.2 Definitions and Generating Functions
    Table 24.2.5: Coefficients b n , k of the Bernoulli polynomials B n ( x ) = k = 0 n b n , k x k .
    k
    Table 24.2.6: Coefficients e n , k of the Euler polynomials E n ( x ) = k = 0 n e n , k x k .
    k