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integral representations for Dirac delta

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1: 1.17 Integral and Series Representations of the Dirac Delta
§1.17(ii) Integral Representations
Other similar integral representations of the Dirac delta that appear in the physics literature include the following:
Bessel Functions and Spherical Bessel Functions (§§10.2(ii), 10.47(ii))
Coulomb Functions (§33.14(iv))
Airy Functions (§9.2)
2: 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). …
3: 33.14 Definitions and Basic Properties
The function s ( ϵ , ; r ) has the following properties: …
4: 9.11 Products
For an integral representation of the Dirac delta involving a product of two Ai functions see §1.17(ii). …
5: Bibliography L
  • Y. T. Li and R. Wong (2008) Integral and series representations of the Dirac delta function. Commun. Pure Appl. Anal. 7 (2), pp. 229–247.
  • 6: 10.22 Integrals
    See also §1.17(ii) for an integral representation of the Dirac delta in terms of a product of Bessel functions. …
    7: 14.30 Spherical and Spheroidal Harmonics
    Explicit Representation
    14.30.8 0 2 π 0 π Y l 1 , m 1 ( θ , ϕ ) ¯ Y l 2 , m 2 ( θ , ϕ ) sin θ d θ d ϕ = δ l 1 , l 2 δ m 1 , m 2 .
    See also (34.3.22), and for further related integrals see Askey et al. (1986). … For a series representation of the product of two Dirac deltas in terms of products of spherical harmonics see §1.17(iii). …