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In Exercise 15, you found the second solution to the Legendre equation for n=0 and n = 1: Qo(x) = Q₁(z) = Since the Q(x) also solve Legendre's equation, they also obey the recursion relations in section 2.2.3 of the LP tutorial. Using these relations, derive Q2(z) and Qs(2), -1. Qa(e) - P₂(x)in((1)) = Qs(e) --P₂(x)in ((1+)²+ =

In Exercise 15, you found the second solution to the Legendre equation for n=0 and n = 1: Qo(x) = Q₁(z) = Since the Q(x) also solve Legendre's equation, they also obey the recursion relations in section 2.2.3 of the LP tutorial. Using these relations, derive Q2(z) and Qs(2), -1. Qa(e) - P₂(x)in((1)) = Qs(e) --P₂(x)in ((1+)²+ =

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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6. In Exercise 15, you found the second solution to the Legendre equation for n = 0 and n = 1; Qo(x) = -log (¹+1), Q₁(z) = log (1+) -1. Since the 2n (*) also solve Legendre's equation, they also obey the recursion relations in section 2.2.3 of the LP tutorial. Using these relations, derive 22(x) and Q3(1). 1 Q₂(x) = P₂ Q3(x) = P₂(x)in ((1+x)) - x 3 2-t Note: 1- P3 (x)in ( ( 1 + x)) - 5 2 5|2 X + 28 X . Remember multiplication of two variables can either be written by using a space or by using* *ory will give you x times y. Note that this is not the same as Ty without a space, that will get read as an entirely different . Remember that your tutorial has Hints in it, at the end of each chapter. If you're stuck, they are often quite usefull
Transcribed Image Text:6. In Exercise 15, you found the second solution to the Legendre equation for n = 0 and n = 1; Qo(x) = -log (¹+1), Q₁(z) = log (1+) -1. Since the 2n (*) also solve Legendre's equation, they also obey the recursion relations in section 2.2.3 of the LP tutorial. Using these relations, derive 22(x) and Q3(1). 1 Q₂(x) = P₂ Q3(x) = P₂(x)in ((1+x)) - x 3 2-t Note: 1- P3 (x)in ( ( 1 + x)) - 5 2 5|2 X + 28 X . Remember multiplication of two variables can either be written by using a space or by using* *ory will give you x times y. Note that this is not the same as Ty without a space, that will get read as an entirely different . Remember that your tutorial has Hints in it, at the end of each chapter. If you're stuck, they are often quite usefull
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