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Chapter 11: Q2P (page 540)
Use the recursion relation (3.4), and if needed, equation (3.2) to simplify:
The value of is .
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Show that the four answers given in Section 1 for are all correct. Hints: For the beta function result, use(6.4). Then get the gamma function results by using (7.1) and the various Γ function formulas. For the elliptic integral, use the hint of Problem 17 with.
Show that for ,and for.
(a) To see the results in Problem 1graphically, computer plot the percentage error in Stirling’s formula as a function of p for values of p = 1-1000. Make separate plots, say for p = 1-10, 10-100, 100-1000, to make it easier to read values from your plots.
(b) Repeat part (a) for the percentage error in (11.5) using two terms of the asymptotic series, that is, Stirling’s formula times.
The logarithmic integralis . Express as exponential integrals
Replace x by ix in (9.1) and let t = iuto show that erf(ix) = ierfi(x), where erfi(x) is defined in (9.7).
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