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Chapter 11: Q11.10P (page 554)
Use Stirling鈥檚 formula to evaluate .
The value of the function is.
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The integral (3.1) is improper because of infinite upper limit and it is also improper for 0 < p < 1 because xp-1becomes infinite at the lower limit. However, the integral is convergent for any p>0. Prove this.
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 sn u, cn u, and dn u, for several values of k, say, for example, .Also plot 3D graphs of sn, cn, and dn as functions of u and k.
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.
3. .
Use the recursion relation (3.4), and if needed, equation (3.2) to simplify:
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