Publisher's Synopsis
Excerpt from Tables of the Inverse Laplace Transform of the Function E-S-Beta
The inverse transform of the function 5 because for these values, the sum of no more than 10 terms of the series in eq (5) suffice to produce g(t) to six-digit accuracy for values of B in the interval For exam ple, if B=0.6 the sum of seven terms of the series gives g(lo) to six places, and the sum of four terms gives g(100) to the same accuracy. Figures la - c contain graphs of g(t) as a function of I over the entire range of tabulated values of B. Note that for B =1 a Dirac delta function which is represented as a vertical line in figure 10.
It is evident, from the curves shown in figure 1, that the g(t) are unimodal. The position of the peak will be denoted by tam. Table 3 contains some val ues of tmax and g(tmn) for the values of B for which we performed our tabulations. It is interesting to observe that among the values of g(tmu) there is a minimum value within the interval Figure 2a shows graphs of tmax and 1/g(tmax) as functions of B for values of B between and 1. The minimum of g(tmu) occurs at tmax=0.252] and is equal to These values correspond to B Figure 2b contains a plot of as a function of tmax. Finally, we have derived polynomial least square approximations to as a function of B. The coefficients of the approximating polynomi als as well as a graphical indication of the degree of agreement with our more accurately calculated values of this function are shown in figure 3. A good approximation to probably requires fitting some function other than a polynomial.
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