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Applied Mathematical Methods by Bhaskar Dasgupta

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Chapter 39

1 The reader is expected to have some background of the tests for convergence of infinite series, and we do not indulge in it right here.

2 or, initial conditions, as noted earlier

3 Noting that our example of the current section is also nothing but an Euler-Cauchy equation, we leave it at this stage. The reader may verify how Frobenius’ method will give the same solution as the method of Chap. 33.

4 Again, without loss of generality, we analyze the case of x0 = 0.

5 At least one Frobenius series solution, corresponding to the larger of r1 and r2 is guaranteed.

6 This is certainly not surprising, particularly because there are complete books on “Bessel functions”!

7 The case of k = l + , even though not an integer, gives r1r2

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