The generating function w (x, t) = (1– 2xt + t2)-1 is given. (a) Show that it satisfies the identity Əw + 2(t – x)w = 0 at (1- 2xt + t2).
The generating function w (x, t) = (1– 2xt + t2)-1 is given. (a) Show that it satisfies the identity Əw + 2(t – x)w = 0 at (1- 2xt + t2).
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
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Chapter6: Topics In Analytic Geometry
Section6.4: Hyperbolas
Problem 5ECP: Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
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![8. The generating function w (x, t) = (1– 2xt + t²)-1 is given.
(a) Show that it satisfies the identity
%3D
(1– 2xt + t2)
+ 2(t – x)w = 0
at
%3D
(b) Substitute the series in problem 7 into the identity in (a)
and derive the recurrence formula (for n = 1, 2, 3, ...)
Un+1(x) – 2xU,(x) + Un-1(x) = 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa279d709-2503-4944-8ec2-0472e9533efc%2Fdd8cb9b8-bfdd-429d-9ee8-23c96d715020%2F0ub0nvu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:8. The generating function w (x, t) = (1– 2xt + t²)-1 is given.
(a) Show that it satisfies the identity
%3D
(1– 2xt + t2)
+ 2(t – x)w = 0
at
%3D
(b) Substitute the series in problem 7 into the identity in (a)
and derive the recurrence formula (for n = 1, 2, 3, ...)
Un+1(x) – 2xU,(x) + Un-1(x) = 0
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