Use the series of to find y.0/ D lim x!0 y.x/ if y.x/ D x2
Chapter , Problem 12(choose chapter or problem)
Use the series of to find y.0/ D lim x!0 y.x/ if y.x/ D x2 " J5=2.x/ C J5=2.x/ J1=2.x/ C J1=2.x/# : Use a computer algebra system to graph y.x/ for x near 0. Does the graph corroborate your value of y.0/? Any integral of the form R xmJn.x/ dx can be evaluated in terms of Bessel functions and the indefinite integral R J0.x/ dx. The latter integral cannot be simplified further, but the function R x 0 J0.t / dt is tabulated in Table 11.1 of Abramowitz and Stegun. Use the identities in Eqs. (22) and (23) to evaluate the integrals in 13 through 21.
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