If n is an integer, use the substitution R(x) = (x) -1/2 Z(x) to show that the
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If n is an integer, use the substitution R(x) = (αx)-1/2Z(x) to show that the general solution of the differential equation
x2R'' + 2xR'' + [α2x2 - n(n + 1)]R = 0
on the interval (0, ∞) is R(x) = c1jn(αx) + c2yn(αx), where jn(αx) and yn(αx) are the spherical Bessel functions of the first and second kind defined in (27).
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Related Book For
A First Course in Differential Equations with Modeling Applications
ISBN: 978-1111827052
10th edition
Authors: Dennis G. Zill
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