Mac Laurin series

This approximation gives better results than the Mac Laurin series, since eq. (3.66) represents the asymptote to the curve, eq. (1.41). The error stays below 1% above an absorbance = 4.7 (2.04 in decadic units). In the range of natural absorbance = 4 to = 4.7 an error less than 2% is obtained. 

Taylor series will yield better results than the Mac Laurin series, eq. (3.65). Beginning at or E one finds [28]... 

Mac Laurin series with only the linear part, Eq. (1-30)]... 

Fig. 4a-b. Total relative activity of enzyme membranes calculated for different cf values in function of the normalized external substrate concentration (number of Si Km) in symmetrical systems (a) with first order reaction (from Goldman et al. [53]) (see Table IV), (b) with no assumption on the order of reaction (calculated by Selegny and Leguillon using 5 term Mac Laurin series of Table VI). 

Concentration profibs calculated in first approximation from truncated Mac Laurin series, approximate solutions of Equation (4 ), are illustrated in Figure 10. It is interesting to note now that the first of the coupled reactions regulates the second one (see caption of Figure 10) and also that the intermediate substrate-product has its concentration quite effectively stabilised within the membrane with regard to concentration variations of the first substrate outside. Densities of enzyme-sites and diffusion properties of the membrane control the stabilised level. 

There are several methods for the development of functions in series, depending on algebraic, trigonometrical, or other processes. The one of greatest utility is known as Taylor s theorem. Mac-laurin s1 theorem is but a special case of Taylor s. We shall work from the special to the general. 

Such functions are useful in the presentation of absorbance-time dependencies. The exponent m will take the values 1, 2, 1/2 and 3/2 in many cases. The disadvantage of these functions is that they contain the parameter. For this reason their use in practise would require extensive tabulations. Another possibility is to develop eq. (1.41) as a power series according to Mac Laurin [10,30-32]... 

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