Using Rodrigues' formula for Pn(x), (T) (i) Pn(-x) = (-1)" P₂(x) cl

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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Using Rodrigues' formula for Pn(x), show that
(T)(i) Pn(-x) = (-1)"Pn(x)
2
(ii) Pn(2)Pm(2) dx = 2n +1
ª dz
-8mn
20+10mm (iv) [+
-1
(ii) P(-x) = (−1)n+¹ P(x)
xPn(x) dx = 0
if n> m.
Transcribed Image Text:Using Rodrigues' formula for Pn(x), show that (T)(i) Pn(-x) = (-1)"Pn(x) 2 (ii) Pn(2)Pm(2) dx = 2n +1 ª dz -8mn 20+10mm (iv) [+ -1 (ii) P(-x) = (−1)n+¹ P(x) xPn(x) dx = 0 if n> m.
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