Chapter 12: Q8-6P (page 562)
Multiply(5.8e)by and integrate from -1 to 1. To evaluate the middle term, integrate by parts.
Chapter 12: Q8-6P (page 562)
Multiply(5.8e)by and integrate from -1 to 1. To evaluate the middle term, integrate by parts.
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Get started for freeUse L23of the Laplace Transform Table (page 469 ) to evaluate .
Expand the following functions in Legendre series.
Expand the following functions in Legendre series.
f(x) = P'n (x).
Hint: For I≥ n, ∫-11 P'n(x)Pl(x) dx=0 (Why?); for l<n, integrate by parts.
Use the Section 15 recursion relations and (17.4) to obtain the following recursion relations for spherical Bessel functions. We have written them for, but they are valid forand for the ,.
Prove the given system of equations and
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