Tables of Relevant Integrals and Other Formulae

In Table Al. 4, standard formulae involving a number of special functions are listed, in some cases as a supplement to the discussion of Sect. A2.4. 

In drawing up these tables, the standard references Gradshteyn and Ryzhik (1965), Abramowitz and Stegun (1970), and Korn and Korn (1968) proved useful, as did Gladwell (1980). 

Note Transforms of polynomials multiplying the functions g x) in (Al.2.5, 6) are given by Golden (1979). 

The incomplete Beta function Bx(a,B) is obtained by replacing the upper integration limit in (2) by x. Note that 

Hilbert transforms, involving T x) and C/ (x), which are given in Table Al.l. Examples 

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Many of these questions can be answered experimentally before a nutrient is added to formulas, but a multilevel, integrated approach is required because of the limitations of human brain analysis (Nelson et al., 2002). The multiple levels of approach are shown in Table 5-10. The integrated approach (see Table 5-11) chosen should be complementary and obey the laws of timing, dose, and duration (Kretchmer et al., 1996). The animal models must be developmentally appropriate with respect to timing of brain events and must coincide with the likely time of nutrient supplementation or deficiency in the human. In other words, for brain-behavior associations to be relevant, the time at which a given nutrient alters brain developmental processes in the animal model should coincide with the time that the nutrient deficit or supplement occurs in the infant population. 

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