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

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

Advanced Engineering Mathematics
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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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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