Unformatted text preview: e.g. p.209 of our text). (a) show that this is a SturmLiouville equation, and ﬁnd the orthogonality relation between the Chebyshev polynomials. (b) following what we did in class to solve Legendre’s equation, obtain the recursion relation for a power series solution to the Chebyshev equation and show that it truncates with the choice k = n 2 (where n is an integer), leading to the Chebyshev polynomials T n ( x ). 3. Derivative of the factorial? Using the deﬁnition of the gamma function Γ( n ), take the derivative d Γ /dn . Can you write the answer in terms of other gamma functions?...
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This note was uploaded on 07/23/2008 for the course MATH 405 taught by Professor Belmonte during the Fall '06 term at Penn State.
 Fall '06
 BELMONTE
 Calculus, Addition

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