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11: 28.28 Integrals, Integral Representations, and Integral Equations
28.28.23 2 π 0 π 𝒞 2 + 2 ( j ) ( 2 h R ) sin ( ( 2 + 2 ) ϕ ) se 2 m + 2 ( t , h 2 ) d t = ( - 1 ) + m B 2 + 2 2 m + 2 ( h 2 ) Ms 2 m + 2 ( j ) ( z , h ) .
§28.28(iv) Integrals of Products of Mathieu Functions of Integer Order
28.28.49 α ^ n , m ( c ) = 1 2 π 0 2 π cos t ce n ( t , h 2 ) ce m ( t , h 2 ) d t = ( - 1 ) p + 1 2 i π ce n ( 0 , h 2 ) ce m ( 0 , h 2 ) h Dc 0 ( n , m , 0 ) .
12: 13.25 Products
For integral representations, integrals, and series containing products of M κ , μ ( z ) and W κ , μ ( z ) see Erdélyi et al. (1953a, §6.15.3).
13: 27.14 Unrestricted Partitions
27.14.2 f ( x ) = m = 1 ( 1 - x m ) = ( x ; x ) , | x | < 1 ,
14: 5.17 Barnes’ G -Function (Double Gamma Function)
5.17.3 G ( z + 1 ) = ( 2 π ) z / 2 exp ( - 1 2 z ( z + 1 ) - 1 2 γ z 2 ) k = 1 ( ( 1 + z k ) k exp ( - z + z 2 2 k ) ) .
15: 14.30 Spherical and Spheroidal Harmonics
For a series representation of the product of two Dirac deltas in terms of products of spherical harmonics see §1.17(iii). …
16: 10.59 Integrals
For an integral representation of the Dirac delta in terms of a product of spherical Bessel functions of the first kind see §1.17(ii), and for a generalization see Maximon (1991). …
17: 26.15 Permutations: Matrix Notation
The inversion number of σ is a sum of products of pairs of entries in the matrix representation of σ : …
18: 14.18 Sums
For a series representation of the Dirac delta in terms of products of Legendre polynomials see (1.17.22). …
19: Bibliography C
  • J. Chen (1966) On the representation of a large even integer as the sum of a prime and the product of at most two primes. Kexue Tongbao (Foreign Lang. Ed.) 17, pp. 385–386.
  • 20: 10.22 Integrals
    See also §1.17(ii) for an integral representation of the Dirac delta in terms of a product of Bessel functions. …