Soal-soal Pertemuan-12
Tugas
Fungsi Bessel
Bessel's Differential Equation
10.26 Show that if x is replaced by λx where λ is a constant, then Bessel’s equation
x 2 y ' '+ xy '+ x 2 − n 2 y = 0 is transformed into x 2 y ' '+ xy '+ λ2 x 2 − n 2 y = 0 .
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Bessel functions of the first kind : Jα
10.27
(a) Show that J1 ( x ) = 2x − 2x2 4 + 22x426 − 22 4x2628 + ... and verity that the interval of
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convergence is − ∞ < x < ∞ .
(b) Show that J 0' ( x ) = − J1 ( x ) .
(c) Show that
d
dx
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[x J1 (x )] = x J 0 (x )
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