Let A and u be positive real numbers. Then Jp(Ax) and Jp(ux) satisfy d d + dx dx (11.6.37) d ( d p² dx dx (11.6.38) respectively. Show that for 2 # µ, | xJp(ax)Jp(ux)dx (11.6.39) 12 - µ2 [Hint: Multiply (11.6.37) by Jp(ux), (11.6.38) by Jp(Ax), subtract the resulting equations and integrate over (0, 1).] If A and u are distinct zeros of Jp(x), what does your result imply?

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Let A and u be positive real numbers. Then Jp(Ax)
and Jp(ux) satisfy
d
d
+
dx
dx
(11.6.37)
d ( d
p²
dx
dx
(11.6.38)
respectively.
Show that for 2 # µ,
| xJp(ax)Jp(ux)dx
(11.6.39)
12 - µ2
[Hint: Multiply (11.6.37) by Jp(ux), (11.6.38)
by Jp(Ax), subtract the resulting equations and
integrate over (0, 1).] If A and u are distinct zeros
of Jp(x), what does your result imply?
Transcribed Image Text:Let A and u be positive real numbers. Then Jp(Ax) and Jp(ux) satisfy d d + dx dx (11.6.37) d ( d p² dx dx (11.6.38) respectively. Show that for 2 # µ, | xJp(ax)Jp(ux)dx (11.6.39) 12 - µ2 [Hint: Multiply (11.6.37) by Jp(ux), (11.6.38) by Jp(Ax), subtract the resulting equations and integrate over (0, 1).] If A and u are distinct zeros of Jp(x), what does your result imply?
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