Show that, defining f* a xmJn(x) dx, m≥n ≥ 0, Im,n(a)= (a) 13,0(x) = [* t³ J(1)dt = x³ J{(x) − 2x²³ h(x); (b) is integrable in terms of Bessel functions and powers of x [such as aº J, (a)] for m+ nodd; (c) may be reduced to integrated terms plus Jo(x) dx for m+n even.
Show that, defining f* a xmJn(x) dx, m≥n ≥ 0, Im,n(a)= (a) 13,0(x) = [* t³ J(1)dt = x³ J{(x) − 2x²³ h(x); (b) is integrable in terms of Bessel functions and powers of x [such as aº J, (a)] for m+ nodd; (c) may be reduced to integrated terms plus Jo(x) dx for m+n even.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![12.1.16 Show that, defining
a
[² xmJn(x) dx, m≥n≥ 0,
Im,n(a)=
(a) 13,0(x) = [*t³ Jo(t)dt = x³ J₁ (x) — 2x² J₂(x);
(b) is integrable in terms of Bessel functions and powers of x [such
as aº J, (a)] for m + nodd;
(c) may be reduced to integrated terms plus foJo(x) dx for m+n
even.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc9a5cafc-08cb-40ec-a2c4-90a7158319c1%2F8b48fb9b-509e-4a12-97f4-11d4da96056d%2Fpnxtmtb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:12.1.16 Show that, defining
a
[² xmJn(x) dx, m≥n≥ 0,
Im,n(a)=
(a) 13,0(x) = [*t³ Jo(t)dt = x³ J₁ (x) — 2x² J₂(x);
(b) is integrable in terms of Bessel functions and powers of x [such
as aº J, (a)] for m + nodd;
(c) may be reduced to integrated terms plus foJo(x) dx for m+n
even.
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