Question 2: Let f possess a continuous nth-order derivative on the interval [—1, 1]. Use Rodrigues' formula and integration by parts to show that 1 L' f(x)P, (x)dx = (1) m² | (x² - f(x)Pn(x)dx (x²-1)" fm (x)dx. ... Question 3: If the functions f₁, f2, fm (not necessarily polynomials) are orthogonal, that is, (fi, fj) = 0 for ij, and if F= c1fi+C2f2+...+cmfm Show that Ck= (F, fk) ||fk||2
Question 2: Let f possess a continuous nth-order derivative on the interval [—1, 1]. Use Rodrigues' formula and integration by parts to show that 1 L' f(x)P, (x)dx = (1) m² | (x² - f(x)Pn(x)dx (x²-1)" fm (x)dx. ... Question 3: If the functions f₁, f2, fm (not necessarily polynomials) are orthogonal, that is, (fi, fj) = 0 for ij, and if F= c1fi+C2f2+...+cmfm Show that Ck= (F, fk) ||fk||2
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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Please siiir please sollllllvvve these 2 questions , thankssss sirr
![Question 2: Let f possess a continuous nth-order derivative on the interval [—1, 1]. Use Rodrigues'
formula and integration by parts to show that
1
L' f(x)P, (x)dx = (1) m² | (x² -
f(x)Pn(x)dx
(x²-1)" fm (x)dx.
...
Question 3: If the functions f₁, f2, fm (not necessarily polynomials) are orthogonal, that is, (fi, fj) = 0
for ij, and if
F= c1fi+C2f2+...+cmfm
Show that
Ck=
(F, fk)
||fk||2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf51e916-9a2e-4c00-a6a7-00cdb77268ec%2F2866a1e1-8296-49dd-a81e-e63955c80d46%2F85z22ml_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 2: Let f possess a continuous nth-order derivative on the interval [—1, 1]. Use Rodrigues'
formula and integration by parts to show that
1
L' f(x)P, (x)dx = (1) m² | (x² -
f(x)Pn(x)dx
(x²-1)" fm (x)dx.
...
Question 3: If the functions f₁, f2, fm (not necessarily polynomials) are orthogonal, that is, (fi, fj) = 0
for ij, and if
F= c1fi+C2f2+...+cmfm
Show that
Ck=
(F, fk)
||fk||2
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