# §14.18 Sums

## §14.18(i) Expansion Theorem

For expansions of arbitrary functions in series of Legendre polynomials see §18.18(i), and for expansions of arbitrary functions in series of associated Legendre functions see Schäfke (1961b).

## §14.18(iii) Other Sums

### ¶ Dougall’s Expansion

For a series representation of the Dirac delta in terms of products of Legendre polynomials see (1.17.22).

## §14.18(iv) Compendia

For collections of sums involving associated Legendre functions, see Hansen (1975, pp. 367–377, 457–460, and 475), Erdélyi et al. (1953a, §3.10), Gradshteyn and Ryzhik (2000, §8.92), Magnus et al. (1966, pp. 178–184), and Prudnikov et al. (1990, §§5.2, 6.5). See also §18.18 and (34.3.19).