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11: 28.28 Integrals, Integral Representations, and Integral Equations
β–Ί
28.28.23 2 Ο€ ⁒ 0 Ο€ π’ž 2 ⁒ β„“ + 2 ( j ) ⁑ ( 2 ⁒ h ⁒ R ) ⁒ sin ⁑ ( ( 2 ⁒ β„“ + 2 ) ⁒ Ο• ) ⁒ se 2 ⁒ m + 2 ⁑ ( t , h 2 ) ⁒ d t = ( 1 ) β„“ + m ⁒ B 2 ⁒ β„“ + 2 2 ⁒ m + 2 ⁑ ( h 2 ) ⁒ Ms 2 ⁒ m + 2 ( j ) ⁑ ( z , h ) .
β–Ί
§28.28(iv) Integrals of Products of Mathieu Functions of Integer Order
β–Ί
28.28.49 Ξ± ^ n , m ( c ) = 1 2 ⁒ Ο€ ⁒ 0 2 ⁒ Ο€ cos ⁑ t ⁒ ce n ⁑ ( t , h 2 ) ⁒ ce m ⁑ ( t , h 2 ) ⁒ d t = ( 1 ) p + 1 ⁒ 2 i ⁒ Ο€ ⁒ ce n ⁑ ( 0 , h 2 ) ⁒ ce m ⁑ ( 0 , h 2 ) h ⁒ Dc 0 ⁑ ( n , m , 0 ) .
12: 13.25 Products
β–ΊFor integral representations, integrals, and series containing products of M ΞΊ , ΞΌ ⁑ ( z ) and W ΞΊ , ΞΌ ⁑ ( z ) see Erdélyi et al. (1953a, §6.15.3).
13: 27.14 Unrestricted Partitions
β–Ί
27.14.2 f ⁑ ( x ) = m = 1 ( 1 x m ) = ( x ; x ) , | x | < 1 ,
14: 5.17 Barnes’ G -Function (Double Gamma Function)
β–Ί
5.17.3 G ⁑ ( z + 1 ) = ( 2 ⁒ Ο€ ) z / 2 ⁒ exp ⁑ ( 1 2 ⁒ z ⁒ ( z + 1 ) 1 2 ⁒ Ξ³ ⁒ z 2 ) ⁒ k = 1 ( ( 1 + z k ) k ⁒ exp ⁑ ( z + z 2 2 ⁒ k ) ) .
15: 14.30 Spherical and Spheroidal Harmonics
β–ΊFor 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
β–ΊFor 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
β–ΊThe inversion number of Οƒ is a sum of products of pairs of entries in the matrix representation of Οƒ : …
18: 14.18 Sums
β–ΊFor a series representation of the Dirac delta in terms of products of Legendre polynomials see (1.17.22). …
19: Bibliography C
β–Ί
  • 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
    β–ΊSee also §1.17(ii) for an integral representation of the Dirac delta in terms of a product of Bessel functions. …