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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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Use (5.4) to show that
(a) if positive integer
(b), where zis not necessarily an integer; see comment after equation (3.3).
In Problem 4 to 13, identify each of the integral as an elliptic (see Example 1 and 2). Learn the notation of your computer program (see Problem 3) and then evaluate the integral by computer.
10. .
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.
Prove that, for positive integral n:
Express the following integrals as functions, and then, by (7.1) , in terms of functions. When possible, use function formulas to write an exact answer in terms of , etc. Compare your answers with computer results and reconcile any discrepancies.
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