The Bessel equation of order zero is x2 y__ + xy_ + x2 y = 0. a. Show that x = 0 is a
Chapter 5, Problem 10(choose chapter or problem)
The Bessel equation of order zero is x2 y__ + xy_ + x2 y = 0. a. Show that x = 0 is a regular singular point. b. Show that the roots of the indicial equation are r1 = r2 = 0. c. Show that one solution for x > 0 is J0( x) = 1 + _ n=1 (1)n x2n 22n(n!)2 . The function J0 is known as the Bessel function of the first kind of order zero. d. Show that the series for J0( x) converges for all x.
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