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Chapter 11: Q11.10P (page 554)
Use Stirling’s formula to evaluate .
The value of the function is.
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Use (5.4) to show that
(a) if positive integer
(b), where zis not necessarily an integer; see comment after equation (3.3).
Computer plot graphs of K(k) and E(k)in (12.3)for k = 0 - 1. Also plot 3Dgraphs of and in (12.1) for k = 0-1andfrom and also from. Warning: Be sure you understand the notation used by your computer program; see text discussion just after (12.3) and Example 1.
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.
and other similar
integrals are called exponential integrals. By making appropriate changes of variable, show that
(Caution:Various notations are used; check carefully the notation in references you
are using.)
Express as a function
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