Laguerre functions definition

The radial functions Sni p) and R i(r) may be expressed in terms of the associated Laguerre polynomials L p), whose definition and mathematical properties are discussed in Appendix F. One method for establishing the relationship between Sniip) and L p) is to relate Sni p) in equation (6.50) to the polynomial L p) in equation (F.15). That process, however, is long and tedious. Instead, we show that both quantities are solutions of the same differential equation. 

For an introduction to Laguerre polynomials, see pages 93-97 of Courant and Hilbert (1956), referenced in Chapter 4. The functions Ajirj, r]") may be regarded as from the tensor product space of L2[0, oo with itself, having an inner product as defined in (6.2.11). For a definition of the tensor product of function spaces, see Ramkrishna and Amundson (1985), referenced in Chapter 4. 

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