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11: 27.4 Euler Products and Dirichlet Series
In this case the infinite product on the right (extended over all primes p ) is also absolutely convergent and is called the Euler product of the series. …
12: 27.14 Unrestricted Partitions
Euler introduced the reciprocal of the infinite productThe 24th power of η ( τ ) in (27.14.12) with e 2 π i τ = x is an infinite product that generates a power series in x with integer coefficients called Ramanujan’s tau function τ ( n ) : …
13: 19.5 Maclaurin and Related Expansions
An infinite series for ln K ( k ) is equivalent to the infinite product
14: 10.21 Zeros
§10.21(iii) Infinite Products
15: 17.2 Calculus
When n in (17.2.35), and when m in (17.2.38), the results become convergent infinite series and infinite products (see (17.5.1) and (17.5.4)). …
16: 10.74 Methods of Computation
For infinite integrals involving products of Bessel functions of the first kind, see Linz and Kropp (1973), Gabutti (1980), Ikonomou et al. (1995), Lucas (1995), and Van Deun and Cools (2008). For infinite integrals involving products of Bessel functions of the first and second kinds, see Ratnanather et al. (2014). …
17: Bibliography R
  • J. T. Ratnanather, J. H. Kim, S. Zhang, A. M. J. Davis, and S. K. Lucas (2014) Algorithm 935: IIPBF, a MATLAB toolbox for infinite integral of products of two Bessel functions. ACM Trans. Math. Softw. 40 (2), pp. 14:1–14:12.
  • R. Roy (2011) Sources in the development of mathematics. Cambridge University Press, Cambridge.
  • 18: 18.1 Notation
    Infinite q -Product
    19: Bibliography L
  • S. K. Lucas (1995) Evaluating infinite integrals involving products of Bessel functions of arbitrary order. J. Comput. Appl. Math. 64 (3), pp. 269–282.
  • 20: 10.43 Integrals
    For infinite integrals of triple products of modified and unmodified Bessel functions, see Gervois and Navelet (1984, 1985a, 1985b, 1986a, 1986b). …