# integral representations for Dirac delta

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## 7 matching pages

##### 1: 1.17 Integral and Series Representations of the Dirac Delta

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###### §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

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►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).
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##### 3: 33.14 Definitions and Basic Properties

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►The function $s(\u03f5,\mathrm{\ell};r)$ has the following properties:
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##### 4: 9.11 Products

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►For an integral representation of the Dirac delta involving a product of two $\mathrm{Ai}$ functions see §1.17(ii).
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##### 5: Bibliography L

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Integral and series representations of the Dirac delta function.
Commun. Pure Appl. Anal. 7 (2), pp. 229–247.
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##### 6: 10.22 Integrals

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►See also §1.17(ii) for an integral representation of the Dirac delta in terms of a product of Bessel functions.
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##### 7: 14.30 Spherical and Spheroidal Harmonics

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###### Explicit Representation

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14.30.8
$${\int}_{0}^{2\pi}{\int}_{0}^{\pi}\overline{{Y}_{{l}_{1},{m}_{1}}(\theta ,\varphi )}{Y}_{{l}_{2},{m}_{2}}(\theta ,\varphi )\mathrm{sin}\theta d\theta d\varphi ={\delta}_{{l}_{1},{l}_{2}}{\delta}_{{m}_{1},{m}_{2}}.$$

►See also (34.3.22), and for further related integrals see Askey et al. (1986).
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►For a series representation of the product of two Dirac deltas in terms of products of spherical harmonics see §1.17(iii).
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