Dirac delta function
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§1.17 Integral and Series Representations of the Dirac Delta… ►In applications in physics and engineering, the Dirac delta distribution (§1.16(iii)) is historically and customarily replaced by the Dirac delta (or Dirac delta function) . …for a suitably chosen sequence of functions , . … ► ►
Airy Functions (§9.2)…
Integral and series representations of the Dirac delta function.
Commun. Pure Appl. Anal. 7 (2), pp. 229–247.
… ►These include, for example, multivalued functions of complex variables, for which new definitions of branch points and principal values are supplied (§§1.10(vi), 4.2(i)); the Dirac delta (or delta function), which is introduced in a more readily comprehensible way for mathematicians (§1.17); numerically satisfactory solutions of differential and difference equations (§§2.7(iv), 2.9(i)); and numerical analysis for complex variables (Chapter 3). …
… ►These are OP’s on the interval with respect to an orthogonality measure obtained by adding constant multiples of “Dirac delta weights” at and to the weight function for the Jacobi polynomials. …
… ►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). …
… ►(For other notation see Notation for the Special Functions.) ►
►The main functions treated in this chapter are first the Coulomb radial functions
, , (Sommerfeld (1928)), which are used in the case of repulsive Coulomb interactions, and secondly the functions
, , , (Seaton (1982, 2002a)), which are used in the case of attractive Coulomb interactions.
Greene et al. (1979):
|Dirac delta; see §1.17.|
, , .