oliverj990
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- Joined
- May 6, 2020
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I'm reading through an article as research for an essay I have been assigned and have found a proof of the Chebyshev Differential Equations being satisfied by Chebyshev polynomials on Wolfram Alpha: https://mathworld.wolfram.com/ChebyshevDifferentialEquation.html
I understand the proof fully up to step 23 but the jump to step 24/26 has confused me since it seems like there should be a denominator term of n! and (n+2)! respectively. The following jumps from 24 to 25/26 to 27 further confuse me as I'm guessing there is some sort of identity/theorem being applied but it has not been stated. The next jump to 28 I understand (summing all possible solutions to the DE) only to be confused by the jump to 29 where it seems another identity or theorem has been applied without clarification. From there onwards I understand but if anyone could help enlighten me regarding the majority of steps between 23 and 29 it would be appreciated!
Thank you
I understand the proof fully up to step 23 but the jump to step 24/26 has confused me since it seems like there should be a denominator term of n! and (n+2)! respectively. The following jumps from 24 to 25/26 to 27 further confuse me as I'm guessing there is some sort of identity/theorem being applied but it has not been stated. The next jump to 28 I understand (summing all possible solutions to the DE) only to be confused by the jump to 29 where it seems another identity or theorem has been applied without clarification. From there onwards I understand but if anyone could help enlighten me regarding the majority of steps between 23 and 29 it would be appreciated!
Thank you
