Chapter 12: Q 5-4 P (page 562)
Use the recursion relation (5.8a) and the values of and to find localid="1664340078504" , and . [After you have found , use it to find and so on for the higher order polynomials.]
Chapter 12: Q 5-4 P (page 562)
Use the recursion relation (5.8a) and the values of and to find localid="1664340078504" , and . [After you have found , use it to find and so on for the higher order polynomials.]
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Get started for freeTo study the approximations in the table, a computer plots on the same axes the given function together with its small approximation and its asymptotic approximation. Use an interval large enough to show the asymptotic approximation agrees with the function for large . If the small approximation is not clear, plot it alone with the function over a small interval .
Solve the differential equations in Problems 5 to 10 by the Frobenius method; observe that you get only one solution. (Note, also, that the two values of are equal or differ by an integer, and in the latter case the larger gives the one solution.) Show that the conditions of Fuchs's theorem are satisfied. Knowing that the second solution is x times the so
Verify that the differential equation in Problemis not Fuchsian. Solve it by separation of variables to find the obvious solutionconst. and a second solution in the form of an integral. Show that the second solution is not expandable in a Frobenius series.
From equation (15.4) show that and
. Then, by Problem 7, show that
for all integral. .
Solve to get . If needed, see Chapter , Section 2. The given equation
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