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1: 27.4 Euler Products and Dirichlet Series
The completely multiplicative function f ( n ) = n - s gives the Euler product representation of the Riemann zeta function ζ ( s ) 25.2(i)): …
2: 25.15 Dirichlet L -functions
25.15.2 L ( s , χ ) = p ( 1 - χ ( p ) p s ) - 1 , s > 1 ,
25.15.4 L ( s , χ ) = L ( s , χ 0 ) p | k ( 1 - χ 0 ( p ) p s ) ,
3: 25.10 Zeros
The product representation (25.2.11) implies ζ ( s ) 0 for s > 1 . …
4: Bibliography R
  • W. H. Reid (1995) Integral representations for products of Airy functions. Z. Angew. Math. Phys. 46 (2), pp. 159–170.
  • W. H. Reid (1997a) Integral representations for products of Airy functions. II. Cubic products. Z. Angew. Math. Phys. 48 (4), pp. 646–655.
  • W. H. Reid (1997b) Integral representations for products of Airy functions. III. Quartic products. Z. Angew. Math. Phys. 48 (4), pp. 656–664.
  • 5: 10.32 Integral Representations
    §10.32(iii) Products
    For collections of integral representations of modified Bessel functions, or products of modified Bessel functions, see Erdélyi et al. (1953b, §§7.3, 7.12, and 7.14.2), Erdélyi et al. (1954a, pp. 48–60, 105–115, 276–285, and 357–359), Gröbner and Hofreiter (1950, pp. 193–194), Magnus et al. (1966, §3.7), Marichev (1983, pp. 191–216), and Watson (1944, Chapters 6, 12, and 13).
    6: 10.9 Integral Representations
    §10.9(iii) Products
    7: 18.17 Integrals
    §18.17(ii) Integral Representations for Products
    Ultraspherical
    Legendre
    For formulas for Jacobi and Laguerre polynomials analogous to (18.17.5) and (18.17.6), see Koornwinder (1974, 1977). …
    8: 9.11 Products
    §9.11(iii) Integral Representations
    For an integral representation of the Dirac delta involving a product of two Ai functions see §1.17(ii). …
    9: Bibliography V
  • H. Volkmer (1984) Integral representations for products of Lamé functions by use of fundamental solutions. SIAM J. Math. Anal. 15 (3), pp. 559–569.
  • 10: 13.12 Products
    For integral representations, integrals, and series containing products of M ( a , b , z ) and U ( a , b , z ) see Erdélyi et al. (1953a, §6.15.3).